Inclusion Criteria:

          -  Written informed consent and HIPAA authorization obtained from the subject and
             documented according to local regulatory requirements prior to beginning any
             protocol-specific procedures, including screening procedures

          -  The subject is willing and able to comply with the protocol for the duration of the
             study including undergoing treatment and scheduled visits and examinations, including
             all follow-up

          -  The subject is medically fit for protocol therapy and competent to give informed
             consent

          -  The subject must have a performance status of 0-1 as determined by criteria set
             forward by ECOG

          -  Subjects with histologically confirmed stage IV any hormone receptor (HR) status/HER2
             negative breast cancer or advanced/recurrent epithelial ovarian cancer

               -  HR positive, HER2 negative breast cancer: patients must have received at least
                  one line of therapy for metastatic disease prior to enrollment, including
                  hormonal therapy and a CDK4/6 inhibitor

               -  HR negative, HER2 negative breast cancer: patients must have received at least
                  one prior line of chemotherapy for metastatic disease

               -  Recurrent, "platinum-sensitive" epithelial ovarian cancer: patients must have
                  received at least two lines of platinum-based chemotherapy prior to enrollment,
                  with at least one of these lines of platinum-based chemotherapy in the recurrent
                  setting

               -  Recurrent, "platinum-resistant" (recurrence within 6 months of a
                  platinum-containing chemotherapy regimen) epithelial ovarian cancer: patients
                  must have received at least one line of platinum-based chemotherapy prior to
                  enrollment

          -  There is pathologic tissue confirming of metastatic breast or ovarian cancer

          -  All adverse events from prior chemotherapy, radiation, or surgery have either returned
             to baseline or are < grade 1 prior to administration of the investigational product

          -  The subject has a body weight of greater than 30kg

          -  The subject must have at the time of screening acceptable hematologic, hepatic, and
             renal function, defined by the following (≤ 28 days prior to registration):

          -  Absolute neutrophil count > 1500/mm3

          -  Hemoglobin > 10g/dL

          -  Platelet count > 100,000/mm3

          -  Creatinine < 1.6 mg/dL

          -  Serum creatinine clearance >40mL/min by the Cockcroft-Gault formula or by 24-hour
             urine collection

          -  Serum bilirubin < 1.5x the upper limit of institutional normal, excluding patients
             with confirmed Gilbert's syndrome (persistent or recurrent hyperbilirubinemia that is
             predominantly unconjugated in the absence of hemolysis or hepatic pathology)

          -  Transaminases (AST/SGOT and ALT/SGPT) < 2.5 times above the upper limits of the
             institutional normal, unless liver metastases are present, in which case it must be <
             5x ULN

          -  INR < 2 for patients who are not on systemic anticoagulation. Patients on
             anticoagulation therapy with an INR > 2 may be enrolled at the discretion of the
             investigator if they have not had any episodes of severe hemorrhage or active bleeding

          -  The subject must be 18 years of age or older

          -  The subject must have not had more than 5 prior lines of cytotoxic chemotherapy in the
             metastatic setting, not including hormonal therapies

          -  Evidence of post-menopausal status, history of hysterectomy or bilateral oophorectomy,
             or negative serum or urine pregnancy test within 7 days prior to starting treatment

               -  Women <50 years of age would be considered post-menopausal if they have been
                  amenorrheic for 12 months or more following cessation of exogenous hormonal
                  treatments and if they have LH and FSH levels in the post-menopausal range for
                  the institution

               -  Women > 50 years of age would be considered post-menopausal if they have been
                  amenorrheic for 12 months or more following cessation of exogenous hormonal
                  treatments, had radiation-induced menopause with last menses >1 year ago, or had
                  chemotherapy-induced menopause with last menses >1 year ago

          -  Women of child-bearing potential must agree to use at least one highly effective form
             of contraception beginning at least 28 days prior to study entry, continuing to do so
             for the duration of their participation in the study, and for 90 days after the last
             dose of study drug. Non-sterilized male partners must also agree to use a male condom
             plus spermicide for the duration of the study. Should a woman become pregnant or
             suspect she is pregnant while participating in this study, she should inform her
             treating physician immediately.

        A female of childbearing potential is any woman (regardless of sexual orientation, having
        undergone a tubal ligation, or remaining celibate by choice) who meets the following
        criteria:

          -  Has not undergone a hysterectomy or bilateral oophorectomy; or

          -  Has not been postmenopausal for at least 12 consecutive months (i.e., has had menses
             at any time in the preceding 12 consecutive months without alternative medical cause),
             as defined above in section 3.1.1

        Exclusion Criteria:

          -  Prior treatment with any investigational drug as part of a clinical trial within 28
             days prior to study drug administration

          -  Concurrent enrolment in another clinical study, unless it is an observational
             (non-interventional) clinical study or during the follow-up period of an
             interventional study

          -  The subject has been treated previously with any anti-PD1/PDL1 therapy, including
             durvalumab

          -  The subject has been previously treated with eribulin

          -  The subject has received a prior anti-cancer therapy (chemotherapy, targeted small
             molecule therapy, endocrine therapy, immunotherapy, biologic therapy, tumor
             embolization, monoclonal antibodies) within 14 days prior to study Day 1

          -  Any concurrent anti-cancer therapy other than denosumab, bisphosphonates, or hormonal
             therapy for non-cancer related conditions

          -  The subject has received radiotherapy treatment to more than 30% of the bone marrow or
             with a wide field of radiation within 28 days of the first dose of study drug

          -  Major surgical procedure within 28 days prior to the first dose of study drug (local
             surgery or isolated lesions for palliative intent is acceptable)

          -  Any unresolved toxicity NCI CTCAE Grade >2 from previous anticancer therapy with the
             exception of alopecia, vitiligo, and lab values which meet inclusion criteria

               -  Subjects with ≤ Grade 2 neuropathy are an exception to this criterion and may
                  qualify for the study as per consultation with the study physician. These
                  patients will require active and continuous monitoring of this toxicity and if
                  any worsening is observed or identified, study drugs will be permanently
                  discontinued immediately

               -  Subjects with irreversible toxicity not reasonably expected to be exacerbated by
                  treatment with eribulin or durvalumab may be included after consultation with the
                  study physician

          -  The subject has a history of, or is reasonably suspected to meet criteria for the
             diagnosis of a known congenital or acquired disorder causing systemic
             immunosuppression or immunodeficiency

          -  The subject has a history of allogeneic organ or bone marrow transplantation

          -  The subject has a history of, or is reasonably suspected to meet criteria for the
             diagnosis of a systemic auto-immune/inflammatory disease or other autoimmune disorder,
             including but not limited to inflammatory bowel disease (Crohn's disease or ulcerative
             colitis), active diverticulitis, systemic lupus erythematosus, Sarcoidosis, Wegener's
             granulomatosis, granulomatosis with polyangiitis, pneumonitis, Grave's disease,
             rheumatoid arthritis, hypophysitis, uveitis.

               -  Exceptions: vitiligo, alopecia, autoimmune-related hypothyroidism which is stable
                  on hormone replacement, chronic skin conditions that do not require systemic
                  therapy, celiac disease controlled with diet alone, or any subjects without
                  active disease in the last 5 years if deemed appropriate by the study physician

          -  Current or prior use of immunosuppressive medication within 28 days before the first
             dose of durvalumab, with the exception of inhaled, local injection, or intranasal
             corticosteroids, systemic steroids at physiological doses (equivalent of ≤ 10mg
             prednisone daily), and steroid premedication for hypersensitivity reactions (e.g., CT
             scan premedication)

          -  The subject has known active central nervous system (CNS) metastases, spinal cord
             compression, and/or leptomeningeal carcinomatosis. Subjects with previously treated
             brain metastases may participate provided they are stable (without evidence of
             progression by imaging for at least 28 days prior to the first dose of trial treatment
             and any neurologic symptoms have returned to baseline), have no evidence of new or
             enlarging brain metastases, and are not using steroids for at least 7 days prior to
             trial treatment. Following radiotherapy and/or surgery for brain metastases subjects
             must wait 4 weeks following the intervention before enrollment to confirm stability.

          -  The subject has a current or past history of active TB (Bacillus Tuberculosis)

          -  The subject has an active infection requiring systemic therapy

          -  The subject has HIV disease (positive HIV 1/2 antibodies)

          -  The subject has active Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV
             RNA [qualitative] PCR is detected). Subjects with a past or resolved HBV infection
             (HBcAb positive and absence of HBsAg reactivity) are eligible

          -  The subject has received a live virus vaccine within 30 days of planned start of study
             therapy Note: Seasonal influenza vaccines for injection are generally inactivated. Flu
             vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist®) are
             live attenuated vaccines, and are not allowed.

          -  The subject has a known additional malignancy that is progressing or requires active
             treatment. Exceptions include non-melanoma cancers of the skin that have been
             resected, in situ malignancies that have been managed with curative therapy and there
             is no current evidence of disease at time of trial enrollment, or history of prior
             malignancy with no known active disease for 5 years prior to trial enrollment

          -  Female patients who are pregnant or breast feeding

          -  Subject is of reproductive potential and is not willing to use effective birth control
             methods from screening for 90 days after the last dose of durvalumab

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to durvalumab or eribulin

          -  Patients who have any severe and/or uncontrolled medical conditions or other
             conditions that could affect their participation in the study including but not
             limited to:

               -  Symptomatic congestive heart failure of New York Heart Association Class III or
                  IV

               -  Mean QT interval corrected for heart rate (QTc) > 470ms calculated from 3
                  electrocardiograms within 15 minutes at 5 minutes apart using Fridericia's
                  Correction

               -  Unstable angina pectoris, uncontrolled hypertension, myocardial infarction within
                  6 months of start of study drug, serious uncontrolled cardiac arrhythmia or any
                  other clinically significant cardiac disease

               -  Interstitial lung disease, or severely impaired lung function as defined as
                  spirometry and DLCO that is 50% of the normal predicted value and/or 02
                  saturation that is 89% or less at rest on room air

               -  Serious chronic gastrointestinal conditions associated with diarrhea

               -  A known or active bleeding diathesis

               -  Psychiatric or substance abuse disorders that would interfere with cooperation
                  with the requirements of the trial or increase risk of adverse events

               -  Uncontrolled diabetes as defined by fasting serum glucose >1.5 x ULN

               -  Active (acute or chronic) or uncontrolled infections

               -  Liver disease such as cirrhosis, chronic active hepatitis or chronic persistent
                  hepatitis