Inclusion Criteria:

          -  Histologically- or cytologically-confirmed diagnosis of locally advanced/unresectable
             (inoperable or not amenable to surgical treatment) and/or metastatic transitional cell
             urothelial cancer of the renal pelvis, ureter, urinary bladder, or urethra

          -  Presence of measurable disease meeting the following criteria:

               -  At least one lesion of >= 1.0 cm in long axis diameter for non-lymph nodes or >=
                  1.5 cm in short axis diameter for lymph nodes that is serially measurable
                  according to RECIST 1.1 using either computerized tomography or magnetic
                  resonance imaging or panoramic and close-up color photography with caliper
                  measurement; if there is only one target lesion and it is a not a lymph node, it
                  should have a long-axis diameter of at least 1.5 cm

               -  Lesions that have had radiotherapy must show radiographic evidence of disease
                  progression based on RECIST 1.1 may be deemed a target lesion

          -  Archival paraffin-embedded invasive tumor tissue or newly obtained biopsy must be
             available prior to the first dose of study drug for biomarker analysis; patients must
             be offered sequential biopsies at baseline and 6 weeks unless in the opinion of the
             trial principal investigator (PI) this would be hazardous; recent data suggest
             discordance between primary tumor and tumor from recurrence or metastasis with high
             percentages of PD-L1 SP142 positive immune cells after recurrence

          -  PD-L1 status determined centrally by HistogeneX, which is funded by the study, must be
             available before randomization of the patient to allow for stratification; COMMERCIAL
             ASSESSMENT OF PD-L1 STATUS OBTAINED LOCALLY AT THE SITE WILL NOT SATISFY ELIGIBILITY
             CRITERIA

          -  New, progressive or recurrent disease occurring

               -  During or within 12 months of treatment with a platinum containing regimen
                  (cisplatin or carboplatin or novel platinum) in either in the metastatic or
                  perioperative setting

               -  In first-line patients defined as cisplatin-ineligible based on renal impairment
                  (creatinine clearance calculated by Cockcroft-Gault method < 60 ml/min), grade 2
                  hearing loss and/or Eastern Cooperative Oncology Group (ECOG) status of 2; these
                  patients will be chemotherapy naive or have received platinum based therapy in
                  the adjuvant or neoadjuvant setting more than 12 months prior to study entry

          -  May have received up to two prior lines of chemotherapy for advanced disease

          -  Adequate recovery from any adverse events resulting from prior anti-neoplastic
             treatment including chemotherapy, biological therapy, targeted small molecule therapy,
             radiation therapy, and surgery as determined by the investigator (and in consultation
             with the study PI); in most instances, adequate recovery is resolution to =< grade 1
             except for alopecia of any grade, grade 2 neuropathy and/ or any grade hearing loss

          -  Subjects with known brain metastases will be eligible if they have completed the
             primary brain therapy (such as whole brain radiotherapy, stereotactic radiosurgery, or
             complete surgical resection) and if they have remained clinically stable,
             asymptomatic, and off of steroids for at least 28 days

          -  Life expectancy of >= 12 weeks

          -  Subjects must have an Eastern Cooperative Oncology Group (ECOG) performance status of
             0 to 2 (Karnofsky >= 60%)

          -  Leukocytes >= 2,500/mcL

          -  Absolute neutrophil count >= 1,500/mcL

          -  Platelets >= 75,000/mcL

          -  Hemoglobin >= 8 g/dL

          -  Total bilirubin =< 1.5 x institutional upper limit of normal (ULN) (however, patients
             with known Gilbert disease who have serum bilirubin level =< 3 x ULN may be enrolled)

          -  Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
             =< 3 x ULN (AST and/or ALT =< 5 x ULN for patients with liver involvement)

          -  Alkaline phosphatase =< 2.5 x ULN (=< 5 x ULN for patients with documented liver
             involvement or bone metastases)

          -  Creatinine clearance >= 20 mL/min/1.73 m^2 by Cockcroft-Gault

          -  International normalized ratio (INR) and activated partial thromboplastin time (aPTT)
             =< 1.5 x ULN (this applies only to patients who do not receive therapeutic
             anticoagulation; patients receiving therapeutic anticoagulation, such as
             low-molecular-weight heparin or warfarin, should be on a stable dose)

          -  All females must have a negative serum or urine pregnancy test (minimum sensitivity 25
             IU/L or equivalent units of beta-human chorionic gonadotropin [B-hCG]) at the
             screening visit and the baseline visit; a pregnancy test needs to be performed within
             72 hours of the first dose of study drug

          -  Administration of atezolizumab and eribulin may have an adverse effect on pregnancy
             and poses a risk to the human fetus, including embryo-lethality; women of
             child-bearing potential and men must agree to use adequate contraception (hormonal or
             barrier method of birth control; abstinence) prior to study entry, for the duration of
             study participation, and for 5 months (150 days) after the last dose of study agent;
             should a woman become pregnant or suspect she is pregnant while she or her partner is
             participating in this study, she should inform her treating physician immediately

          -  Male subjects who are partners of women of childbearing potential must use a condom
             and spermicide and their female partners if of childbearing potential must use a
             highly effective method of contraception beginning at least 1 menstrual cycle prior to
             starting study drug(s), throughout the entire study period, and for 150 days after the
             last dose of study drug, unless the male subjects are totally sexually abstinent or
             have undergone a successful vasectomy with confirmed azoospermia or unless the female
             partners have been sterilized surgically or are otherwise proven sterile

          -  Ability to understand and the willingness to sign a written informed consent document

          -  Subject must be willing and able to comply with all aspects of the protocol

          -  Patients positive for human immunodeficiency virus (HIV) are allowed on study, but
             HIV-positive patients must have:

               -  A stable regimen of highly active anti-retroviral therapy (HAART) using
                  combination retroviral agents which are not CYP3A4 inducers or inhibitors

               -  No requirement for concurrent antibiotics or antifungal agents for the prevention
                  of opportunistic infections

               -  A CD4 count above 250 cells/mcL and an undetectable HIV viral load on standard
                  polymerase chain reaction (PCR)-based tests

        Exclusion Criteria:

          -  Patients with prior allogeneic bone marrow transplantation or prior solid organ
             transplantation

          -  Patients who have had chemotherapy within 3 weeks or radiotherapy or targeted therapy
             2 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those
             who have not recovered from adverse events (other than alopecia) due to agents
             administered more than 4 weeks earlier; however, the following therapies are allowed:

               -  Hormone-replacement therapy or oral contraceptives

               -  Herbal therapy > 1 week prior to cycle 1, day 1 (herbal therapy intended as
                  anticancer therapy must be discontinued at least 1 week prior to cycle 1, day 1)

               -  Palliative radiotherapy for bone metastases > 2 weeks prior to cycle 1, day 1

          -  Prior treatment with anti-PD-1, or anti-PD-L1 therapeutic antibody or
             pathway-targeting agents or eribulin

               -  Patients who have received prior treatment with anti-CTLA-4 may be enrolled,
                  provided the following requirements are met:

                    -  Minimum of 12 weeks from the first dose of anti-CTLA-4 and > 6 weeks from
                       the last dose

                    -  No history of severe immune-related adverse effects from anti-CTLA-4
                       (National Cancer Institute [NCI] Common Terminology Criteria for Adverse
                       Events [CTCAE] version 5.0)

          -  Treatment with any other investigational agent within 4 weeks prior to cycle 1, day 1

          -  Treatment with systemic immunostimulatory agents (including, but not limited to,
             interferon [IFN]-alpha or interleukin [IL]-2) within 6 weeks prior to cycle 1, day 1

          -  Treatment with systemic immunosuppressive medications (including, but not limited to,
             prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor
             necrosis factor [anti-TNF] agents) within 2 weeks prior to cycle 1, day 1

               -  Patients who have received acute, low dose, systemic immunosuppressant
                  medications (e.g., a one-time dose of dexamethasone for nausea) may be enrolled

               -  The use of inhaled corticosteroids and mineralocorticoids (e.g., fludrocortisone)
                  for patients with orthostatic hypotension or adrenocortical insufficiency is
                  allowed

          -  Patients taking bisphosphonate therapy for symptomatic hypercalcemia; use of
             bisphosphonate therapy for other reasons (e.g., bone metastasis or osteoporosis) is
             allowed

          -  Patients requiring treatment with a receptor activator of nuclear factor kappa-B
             ligand (RANKL) inhibitor (e.g. denosumab) who cannot discontinue it before treatment
             with atezolizumab

          -  Patients with known primary central nervous system (CNS) malignancy or symptomatic CNS
             metastases are excluded, with the following exceptions:

               -  Patients with asymptomatic untreated CNS disease may be enrolled, provided all of
                  the following criteria are met:

                    -  Evaluable or measurable disease outside the CNS

                    -  No metastases to brain stem, midbrain, pons, medulla, cerebellum, or within
                       10 mm of the optic apparatus (optic nerves and chiasm)

                    -  No history of intracranial hemorrhage or spinal cord hemorrhage

                    -  No ongoing requirement for dexamethasone for CNS disease; patients on a
                       stable dose of anticonvulsants are permitted

                    -  No neurosurgical resection or brain biopsy within 28 days prior to cycle 1,
                       day 1

               -  Patients with asymptomatic treated CNS metastases may be enrolled, provided all
                  the criteria listed above are met as well as the following:

                    -  Radiographic demonstration of improvement upon the completion of CNS
                       directed therapy and no evidence of interim progression between the
                       completion of CNS directed therapy and the screening radiographic study

                    -  No stereotactic radiation or whole-brain radiation within 28 days prior to
                       cycle 1, day 1

                    -  Screening CNS radiographic study >= 4 weeks from completion of radiotherapy
                       and >= 2 weeks from discontinuation of corticosteroids

          -  Known hypersensitivity to Chinese hamster ovary cell products or other recombinant
             human antibodies

          -  History of severe allergic, anaphylactic, or other hypersensitivity reactions to
             chimeric or humanized antibodies or fusion proteins or eribulin

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to other agents used in study

          -  Known additional malignancy that is progressing or requires active treatment excepting
             basal cell carcinoma of the skin, squamous cell carcinoma of the skin that has
             undergone potentially curative therapy, or in situ cancer; patients with another known
             malignancy are allowed as long that other cancer is in clinical remission for at least
             2 years prior to cycle 1 (C1) day 1 (D1)

          -  History of significant cardiovascular disease, defined as:

               -  Congestive heart failure greater than New York Heart Association (NYHA) class III
                  according to the NYHA functional classification

               -  Unstable angina or myocardial infarction within 6 months of enrollment

               -  Serious cardiac arrhythmia

               -  A prolonged QT/corrected QT (QTc) interval (QTc > 500 ms) demonstrated on
                  electrocardiogram (ECG) at screening or baseline; a history of risk factors for
                  torsade de pointes (e.g., heart failure, hypokalemia, family history of long QT
                  syndrome) or the use of concomitant medications that prolonged the QT/QTc
                  interval

          -  Autoimmune disease that has required systemic treatment in past 2 years

          -  Clinically significant illness that requires medical treatment within 8 weeks or a
             clinically significant infection that requires medical treatment within 4 weeks of
             dosing

          -  History of organ allograft

          -  Active hepatitis b virus (positive hepatitis b surface antigen) or active hepatitis c
             virus (measurable viral ribonucleic acid [RNA] load with polymerase chain reaction)
             infection

          -  Known intolerance to either of the study drugs (or any of the excipients)

          -  Any medical or other condition which, in the opinion of the investigator, would
             preclude participation in a clinical trial or the investigator's belief that the
             subject is medically unfit to receive eribulin mesylate and atezolizumab or unsuitable
             for any other reason

          -  Known clinically significant liver disease, including active viral, alcoholic, or
             other hepatitis; cirrhosis; fatty liver; and inherited liver disease

               -  Patients with past or resolved hepatitis B infection (defined as having a
                  negative hepatitis B surface antigen [HBsAg] test and a positive anti-HBc
                  [antibody to hepatitis B core antigen] antibody test) are eligible

               -  Patients positive for hepatitis C virus (HCV) antibody are eligible only if
                  polymerase chain reaction (PCR) is negative for HCV RNA

          -  History or risk of autoimmune disease, including, but not limited to, systemic lupus
             erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis
             associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjogren's
             syndrome, Bell's palsy, Guillain-Barre syndrome, multiple sclerosis, autoimmune
             thyroid disease, vasculitis, or glomerulonephritis

               -  Patients with a history of autoimmune hypothyroidism on a stable dose of thyroid
                  replacement hormone may be eligible

               -  Patients with controlled type 1 diabetes mellitus on a stable insulin regimen may
                  be eligible

               -  Patients with eczema, psoriasis, lichen simplex chronicus of vitiligo with
                  dermatologic manifestations only (e.g., patients with psoriatic arthritis would
                  be excluded) are permitted provided that they meet the following conditions:

                    -  Patients with psoriasis must have a baseline ophthalmologic exam to rule out
                       ocular manifestations

                    -  Rash must cover less than 10% of body surface area (BSA)

                    -  Disease is well controlled at baseline and only requiring low potency
                       topical steroids (e.g., hydrocortisone 2.5%, hydrocortisone butyrate 0.1%,
                       fluocinolone 0.01%, desonide 0.05%, alclometasone dipropionate 0.05%)

                    -  No acute exacerbations of underlying condition within the last 12 months
                       (not requiring psoralen plus ultraviolet A radiation [PUVA], methotrexate,
                       retinoids, biologic agents, oral calcineurin inhibitors; high potency or
                       oral steroids)

          -  History of idiopathic pulmonary fibrosis, pneumonitis (including drug induced),
             organizing pneumonia (i.e., bronchiolitis obliterans, cryptogenic organizing
             pneumonia, etc.), or evidence of active pneumonitis on screening chest computed
             tomography (CT) scan; history of radiation pneumonitis in the radiation field
             (fibrosis) is permitted

          -  Patients with active tuberculosis (TB) are excluded

          -  Severe infections within 4 weeks prior to cycle 1, day 1, including, but not limited
             to, hospitalization for complications of infect