Inclusion Criteria:

          -  Patients must have documented EWSR1/ATF1 or EWSR1/CREB1 translocation or
             histologically confirmed clear cell sarcoma, documented grade 2 or 3 conventional
             chondrosarcoma, or documented dedifferentiated chondrosarcoma. The disease must not be
             curable by surgery

          -  Patients must have measurable disease, defined as at least one lesion that can be
             accurately measured in at least one dimension (longest diameter to be recorded for
             non-nodal lesions and short axis for nodal lesions) as >= 20 mm (>= 2 cm) by chest
             x-ray or as >= 10 mm (>= 1 cm) with computed tomography (CT) scan, magnetic resonance
             imaging (MRI), or calipers by clinical exam

          -  Patients with newly diagnosed, unresectable, metastatic and measurable clear cell
             sarcoma, EWSR1/ATF1 or EWSR1/CREB1 translocation, grade 2 or 3 conventional
             chondrosarcoma, or dedifferentiated chondrosarcoma will also be eligible if they show
             clinical evidence of disease progression (including history and increasing physical
             symptoms). On-study documentation will include a physician's rationale that supports
             evidence of clinical disease progression (i.e., increasing tumor pain)

          -  Age >= 2 years at the National Cancer Institute (NCI) Clinical Center (>= 12 years at
             other participating sites)

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 2 (Karnofsky or Lansky
             >= 70%)

          -  Life expectancy of greater than 3 months

          -  Absolute neutrophil count >= 1,000/mcL

          -  Platelets >= 100,000/mcL

          -  Hemoglobin >= 8 g/dL

          -  Total bilirubin =< 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 institutional 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:

               -  For adult patients (>= 18 years of age): >= 30 mL/min/1.73 m^2 by Cockcroft-Gault

               -  For pediatric patients (< 18 years of age), a serum creatinine based on age and
                  gender as follows:

                    -  Age: 2 to < 6 years; Maximum serum creatinine (mg/dL): 0.8 (male) 0.8
                       (female)

                    -  Age: 6 to < 10 years; Maximum serum creatinine (mg/dL): 1 (male) 1 (female)

                    -  Age: 10 to < 13 years; Maximum serum creatinine (mg/dL): 1.2 (male) 1.2
                       (female)

                    -  Age: 13 to < 16 years; Maximum serum creatinine (mg/dL): 1.5 (male) 1.4
                       (female)

                    -  Age: 16 to < 18 years; Maximum serum creatinine (mg/dL): 1.7 (male) 1.4
                       (female)

          -  Patients with treated brain metastases are eligible if follow-up brain imaging after
             central nervous system (CNS)-directed therapy shows no evidence of progression for >=
             1 month after treatment of the brain metastases

          -  Patients with new or progressive brain metastases (active brain metastases) or
             leptomeningeal disease are eligible if the treating physician determines that
             immediate CNS-specific treatment is not required and is unlikely to be required during
             the first 2 cycles of therapy

          -  Patients with a prior malignancy whose natural history or treatment does not have the
             potential to interfere with the safety or efficacy assessment of the investigational
             regimen are eligible for this trial

          -  Patients with known history or current symptoms of cardiac disease, or history of
             treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac
             function using the New York Heart Association Functional Classification. To be
             eligible for this trial, patients should be class 2B or better

          -  Willingness to provide biopsy samples for research purposes (patients >= 18 years of
             age only)

          -  Administration of atezolizumab may have an adverse effect on pregnancy and poses a
             risk to the human fetus, including embryo-lethality. Female patients of child-bearing
             potential and male patients 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

          -  Ability to understand and the willingness to sign a written informed consent document
             or a parent/guardian able to do the same

        Exclusion Criteria:

          -  Any prior therapy must have been completed >= 4 weeks or, if known, >= 5 half-lives of
             the prior agent (whichever is shorter) prior to enrollment on protocol (minimum of 1
             week between prior therapy and study enrollment), and the participant must have
             recovered to eligibility levels from prior toxicity. Patients should be at least 6
             weeks out from nitrosoureas and mitomycin C. Prior definitive radiation should have
             been completed >= 4 weeks or palliative radiation should have been completed >= 2
             weeks prior to study enrollment and all associated toxicities resolved to eligibility
             levels (patients on study may be eligible for palliative radiotherapy to non-targeted
             lesions after 2 cycles of therapy at the principal investigator [PI's] discretion).
             Patients who have had prior monoclonal antibody therapy must have completed that
             therapy >= 6 weeks (or 3 half-lives of the antibody, whichever is shorter) prior to
             enrollment on protocol (minimum of 1 week between prior therapy and study enrollment).
             A patient who has received a cumulative dose of > 350 mg/m^2 of anthracycline
             (regardless of cardioprotectant) may only be enrolled if their ejection fraction
             measured by an echocardiogram is within normal institutional limits

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

               -  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 (NCI
                       Common Terminology Criteria for Adverse Events [CTCAE] grade 3 and 4)

          -  Treatment with any other investigational agent within 4 weeks (or within five half
             lives of the investigational product, whichever is shorter) prior to cycle 1, day 1
             (minimum of 1 week between prior therapy and study enrollment). Patients must be >= 2
             weeks since any investigational agent administered as part of a phase 0 study (also
             referred to as an "early phase I study" or "pre-phase I study" where a sub-therapeutic
             dose of drug is administered) at the coordinating center PI's discretion, and should
             have recovered to eligibility levels from any toxicities

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

          -  Treatment with systemic immunosuppressive medications (including, but not limited to,
             prednisone [ > 10 mg/day], 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 systemic 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

          -  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 (i.e., antibodies with generic names ending in
             "ximab" or "zumab", respectively) or fusion proteins

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac
             arrhythmia, or psychiatric illness/social situations that would limit compliance with
             study requirements

          -  Pregnant women are excluded from this study because atezolizumab is an investigational
             agent with the unknown potential for teratogenic or abortifacient effects. Because
             there is an unknown but potential risk for adverse events in nursing infants secondary
             to treatment of the mother with atezolizumab, breastfeeding should be discontinued if
             the mother is treated with atezolizumab

          -  Patients with a history of human immunodeficiency virus (HIV)-positive on
             antiretroviral therapy are eligible with an undetectable viral load. For those
             patients, an HIV viral load test must be completed within 28 days prior to enrollment

          -  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 ribonucleic acid (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 autoimmune hyperthyroid disease not requiring immunosuppressive
                  treatment 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, or 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 infection, bacteremia, or severe pneumonia

          -  Signs or symptoms of infection within 2 weeks prior to cycle 1, day 1

          -  Received oral or intravenous (IV) antibiotics within 2 weeks prior to cycle 1, day 1.
             Patients receiving prophylactic antibiotics (e.g., for prevention of a urinary tract
             infection or chronic obstructive pulmonary disease) are eligible

          -  Major surgical procedure within 28 days prior to cycle 1, day 1 or anticipation of
             need for a major surgical procedure during the course of the study

          -  Administration of a live, attenuated vaccine within 4 weeks before cycle 1, day 1 or
             anticipation that such a live, attenuated vaccine will be required during the study
             and up to 5 months after the last dose of atezolizumab

               -  Influenza vaccination should be given during influenza season only (approximately
                  October to March). Patients must not receive live, attenuated influenza vaccine
                  within 4 weeks prior to cycle 1, day 1 or at any time during the study