A Phase II Study of Eribulin and Pembrolizumab in Soft Tissue Sarcomas

Inclusion Criteria: * Histologically confirmed liposarcoma, leiomyosarcoma, or undifferentiated/unclassified pleomorphic sarcoma by a Dana-Farber Cancer Institute or Massachusetts General Hospital pathologist * Participants 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 with conventional techniques or as ≥10 mm with spiral CT scan, MRI, or calipers by clinical exam. See Section 11 for the evaluation of measurable disease. * Participants must have received at least one prior line of chemotherapy. No limit on prior lines of therapy. * Age ≥ 18 years. * ECOG performance status of 0 or 1 (see Appendix A). * Participants must have normal organ and marrow function as defined below: * leukocytes ≥3,000/mcL * absolute neutrophil count ≥1,500/mcL * platelets ≥100,000/mcL * Hemoglobin ≥ 8 g/dL within the first 2 weeks prior to the first dose of study drugs, transfusion is allowed. * total bilirubin ≤1.5× institutional upper limit of normal (ULN) (except participants with Gilbert Syndrome, who can have total bilirubin \<3.0 mg/dL) * AST(SGOT)/ALT(SGPT)\<2.5 x ULN in a participant with no documented liver metastases; ALT and AST \<5.0 x ULN in a participant with documented liver metastases * creatinine ≤1.5× ULN OR * creatinine clearance ≥50 mL/min/1.73 m2 for participants with creatinine levels above institutional normal (using the Cockcroft-Gault Formula below): * Female CrCl = (140 - age in years) x weight in kg x 0.85 72 x serum creatinine in mg/dL * Male CrCl = (140 - age in years) x weight in kg 72 x serum creatinine in mg/dL * Available archival tumor tissue including Formalin-fixed, paraffin embedded (FFPE) or fresh frozen, or be willing to undergo baseline biopsy for tumor tissue correlative biomarker studies. * The effects of eribulin and pembrolizumab on the developing human fetus are unknown. For this reason, women of child-bearing potential (WOCBP) and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. A male participant must agree to use a contraception as detailed in Appendix G of this protocol during the treatment period and for at least 20 weeks, corresponding to the time needed to eliminate any study treatments, plus an additional 120 days (a spermatogenesis cycle) after the last dose of study treatment. A female participant is eligible to participate if she is not pregnant (see Appendix G), not breastfeeding, and at least one of the following conditions applies: * Not a woman of childbearing potential (WOCBP) as defined in Appendix G OR * A WOCBP who agrees to follow the contraceptive guidance in Appendix G during the treatment period and for at least 20 weeks plus an additional 30 days (a menstruation cycle) after the last dose of study treatment. * WOCBP should use an adequate method to avoid pregnancy for at least 20 weeks plus an additional 30 days after the last dose of investigational drug. Women of childbearing potential must have a negative serum pregnancy test within 72 hours prior to the start of Eribulin and Pembrolizumab. Women must not be breastfeeding. Women who are not of childbearing potential (i.e., who are postmenopausal or surgically sterile) do not require contraception. Women of childbearing potential (WOCBP) is defined as any female who has experienced menarche and who has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy) or who is not postmenopausal. Menopause is defined clinically as 12 months of amenorrhea in a woman over 45 in the absence of other biological or physiological causes. In addition, women under the age of 55 must have a documented serum follicle stimulating hormone (FSH) level less than 40 mIU/mL. * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Participants who have had standard chemotherapy or radiotherapy within 3 weeks prior to entering the study. * Participants who have not recovered from adverse events (grade 2 or higher toxicities) due to agents administered, radiotherapy, or surgery more than 3 weeks earlier, with the exception of alopecia. * Previous treatment with eribulin or any anti-PD-1, PD-L1, or PD-L2 agent, or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (eg, CTLA-4, OX 40, CD137). * Participants who are currently participating in or have participated in a study of an investigational agent or have used an investigational device within 3 weeks prior to the first dose of study treatment. * Note: Participants who have entered the follow-up phase of an investigational study may participate as long as it has been 3 weeks after the last dose of the previous investigational agent. * 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 have not experienced any new neurologic symptoms for the last 4 weeks prior to study entry, and have recovered from the effects of radiotherapy or surgery. There must also be no requirement for immunosuppressive doses of systemic corticosteroids (\>10 mg/day prednisone equivalents) for at least 2 weeks prior to study drug administration. Treatment for brain metastases may have included whole brain radiotherapy, radiosurgery, surgery, or a combination as deemed appropriate by the treating physician. * Have received a live vaccine within 30 days prior to the first dose of study drug. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guérin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (eg, FluMist®) are live attenuated vaccines and are not allowed. * Inability to comply with study and/or follow-up procedures. * History of severe hypersensitivity reaction (≥Grade 3) to any monoclonal antibody. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to Eribulin or Pembrolizumab. * 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 which in the PI's opinion makes it undesirable for the participant to participate in the trial or which would jeopardize compliance with the trial and study requirements. * Pregnant women (WOCBP who had a positive serum pregnancy test on screening or 72 hours prior to initiation of study protocol) are excluded from this study because the effects of Eribulin and Pembrolizumab on the developing fetus are unknown. There is the 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 Eribulin and Pembrolizumab, breastfeeding should be discontinued if the mother is treated with Eribulin and Pembrolizumab. * Because the effects of pembrolizumab on chronic viral infection are not well known, participants should be excluded if they have known history of testing positive for human immunodeficiency virus (HIV) (true positive) or known acquired immunodeficiency syndrome (AIDS) or if they have a positive test for hepatitis B virus surface antigen (HBV sAg) or hepatitis C virus ribonucleic acid (HCV antibody) indicating acute or chronic infection. * Participants with active autoimmune disease or history of autoimmune disease that might recur, which may affect vital organ function or require immune suppressive treatment including systemic corticosteroids, are excluded. These include but are not limited to participants with a history of immune related neurologic disease such as multiple sclerosis, autoimmune (demyelinating) neuropathy, Guillain-Barre syndrome, or myasthenia gravis; participants with a history of systemic autoimmune disease such as SLE, connective tissue diseases, scleroderma, inflammatory bowel disease (IBD), Crohn's, ulcerative colitis, or hepatitis; and participants with a history of toxic epidermal necrolysis (TEN), Stevens-Johnson syndrome, or phospholipid syndrome. These participants should be excluded because of the risk of recurrence or exacerbation of disease. Participants with vitiligo or endocrine deficiencies, including thyroiditis managed with replacement hormones such as physiologic corticosteroids, are eligible. Participants with rheumatoid arthritis or other arthropathies; Sjögren's syndrome; psoriasis controlled with topical medication; or participants with positive serology, such as antinuclear antibodies (ANA) or anti-thyroid antibodies, should be evaluated for the presence of target organ involvement and potential need for systemic treatment but should otherwise be eligible. * Participants are permitted to enroll if they have vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger (precipitating event). * Participants should be excluded if they have a condition requiring systemic treatment with either corticosteroids (\>10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration. Inhaled or topical steroids and adrenal replacement doses \<10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease. Participants are permitted to use topical, ocular, intraarticular, intranasal, and inhalational corticosteroids (with minimal systemic absorption). Physiologic replacement doses of systemic corticosteroids are permitted, even if \<10 mg/day prednisone equivalents. A brief course of corticosteroids for prophylaxis (e.g., contrast dye allergy) or for treatment of non-autoimmune conditions (e.g., delayed-type hypersensitivity reaction caused by contact allergen) is permitted. * Participants with a history of pneumonitis or interstitial lung disease. * History of primary immunodeficiency or solid organ transplantation. * Participants who have had evidence of active or acute diverticulitis, intra-abdominal abscess, GI obstruction, or fistula or abdominal carcinomatosis (which are known risk factors for bowel perforation) should be evaluated for the potential need for additional treatment before coming on study.