A Randomized Phase II Study Of Eribulin Mesylate With or Without Pembrolizumab For Metastatic Hormone Receptor Positive Breast Cancer

Inclusion Criteria * Patients must have histologically or cytologically confirmed Stage IV invasive breast cancer. Patients without pathologic or cytologic confirmation of metastatic disease should have unequivocal evidence of metastasis from physical examination or radiologic evaluation. * Subjects must have at least one lesion that is not within a previously radiated field that is evaluable on computerized tomography (CT) or magnetic resonance imaging (MRI) scan per RECIST version 1.1. If the subject's only evaluable disease is within a previously radiated field, it must have demonstrated progression since the time of radiation. * Participants must have HR positive, HER2-negative breast cancer (ER\>1% and/or, PR\>1%, HER2-negative per ASCO CAP guidelines, 2013 resulted on the primary tumor and/or a metastatic lesion). * Participants must have already received or been intolerant to at least two lines of hormonal therapies (including the adjuvant or metastatic setting) or be appropriate candidates for chemotherapy * Prior chemotherapy: Participants are allowed to have received up to 2 prior lines of chemotherapy in the metastatic setting. If a prior chemotherapy was given for less than 1 cycle, it will not be counted as a prior line. The last dose of chemotherapy must be ≥14 days prior to initiation of study therapy. Participants should be adequately recovered from acute toxicities of prior treatment. No prior treatment with eribulin mesylate is allowed. * Prior biologic therapy: The last dose of biologic or investigational therapy must be ≥21 days prior to initiation of study therapy. * Prior hormonal therapy: Hormonal therapy must have been discontinued ≥14 days prior to initiation of study therapy. However, continuation of ovarian suppression is allowed. * Prior radiation therapy: Participants may have received prior radiation therapy in either the metastatic or early-stage setting. Radiation therapy must be completed ≥14 days prior to initiation of study therapy. * Prior targeted therapy: Targeted therapy must have been discontinued ≥ 14 days prior to initiation of study therapy. * Biphosphonates/Denosumab: Participants on bisphosphonates/denosumab may continue receiving bisphosphonate therapy during study treatment. * Participants must have an archival tumor sample available (1 block or 20 unstained slides). If no archival tissue is available, participants must be willing to undergo a research biopsy of their disease if it is safely accessible. * Age ≥ 18 years of age * ECOG performance status ≤2 (Karnofsky ≥60%) * Participants must have normal organ and marrow function as defined below: * absolute neutrophil count ≥1,500/mcL * platelets ≥100,000/mcL * hemoglobin ≥ 8 g/dl * total bilirubin ≤1.5 × institutional upper limit of normal (ULN) * AST(SGOT)/ALT(SGPT) ≤2.5 × institutional ULN (≤ 5 × institutional ULN with documented liver metastases, * serum creatinine ≤1.5mg/dL or calculated GFR ≥60 mL/min * INR/PT ≤1.5 times ULN unless participant is receiving anticoagulant therapy, as long as PT or PTT is within therapeutic range of intended use of anticoagulants * aPTT/PTT ≤1.5 times ULN unless participant is receiving anticoagulant therapy, as long as PT or PTT is within therapeutic range of intended use of anticoagulants * The effects of eribulin mesylate and pembrolizumab on the developing human fetus are unknown. Pre-clinical data was suggestive of a teratogenic effect of eribulin mesylate. For these reasons women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) for the duration of study participation and 4 months after the last dose of eribulin mesylate and/or pembrolizumab. Note: abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject. * Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, the treating physician and principal investigator should be informed immediately. * While on the study, women must not breastfeed. * Subjects of childbearing potential are defined as those who have not been surgically sterilized and/or have had a menstrual period in the past year * Female subjects of childbearing potential, as defined above, must have a either a negative urine or a negative serum pregnancy test within seven (7) days of first dose of pembrolizumab. If a urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. * Ability to understand and willingness to sign a written informed consent document. Exclusion Criteria * Chemotherapy-related or radiation-related toxicities that have not resolved to Grade 1 severity or lower, except for stable sensory neuropathy (≤ Grade 2) and alopecia. * Participants who are receiving any other investigational agents. * Previous treatment with eribulin mesylate or any anti-PD-1, PD-L1, or PD-L2 agent or participation in any MK-3475 Merck studies. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to eribulin mesylate or pembrolizumab. * Known brain metastases that are untreated, symptomatic, or require therapy to control symptoms. Participants with previously diagnosed brain metastases are eligible if they have completed treatment at least 4 weeks prior to registration, are neurologically stable and absence of new neurologic symptoms for the last 4 weeks prior to study entry, and have recovered from the effects of radiotherapy or surgery. Any corticosteroid use for brain metastases must have been discontinued without the subsequent appearance of symptoms for ≥2 weeks before the first study drug. Treatment for brain metastases may have included whole brain radiotherapy, radiosurgery, or a combination as deemed appropriate by the treating physician. * Uncontrolled intercurrent illness, including, but not limited to uncontrolled hypertension, unstable angina pectoris, uncontrolled cardiac arrhythmia, congestive heart failure-New York Heart Association Class III or IV, active ischemic heart disease, myocardial infarction within the previous six months, uncontrolled diabetes mellitus, gastric or duodenal ulceration diagnosed within the previous 6 months, chronic liver or renal disease, severe malnutrition or psychiatric illness/social situations that would limit compliance with study requirements. * Clinically significant electrocardiogram (ECG) abnormality, including a marked baseline prolonged QT/QTc (\[QT interval/corrected QT interval\], eg, a repeated demonstration of a QTc interval \>500 ms). * Medcial condition that requires chronic systemic steroid therapy or on any other form of immunosuppressive medication. For example, participants with autoimmune disease that requires systemic steroids or immunosuppression agents should be excluded. Replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. * History or evidence of active, noninfectious pneumonitis that required treatment with steroids. * History of interstitial lung disease. * Participants known to be positive for the human immunodeficiency virus (HIV), Hepatitis B antigen (HepBsAg), or Hepatitis C virus (HCV) RNA. HIV-positive participants on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with Pembrolizumab and/or eribulin mesylate. In addition, these participants are at increased risk of lethal infections. * Individuals with a history of a second malignancy are ineligible except for the following circumstances. Individuals with a history of other malignancies are eligible if they have been disease-free for at least 5 years and are deemed by the investigator to be at low risk for recurrence of that malignancy. Individuals with the following cancers are eligible if diagnosed and treated within the past 5 years: cervical cancer in situ, and non-melanoma cancer of the skin. Patients with other cancers diagnosed within the past 5 years and felt to be at low risk of recurrence should be discussed with the study sponsor to determine eligibility. * Has received a live vaccine within 28 days of planned start of study therapy.