A Phase II of Nivolumab Plus Ipilimumab in Non-resectable Sarcoma and Endometrial Carcinoma

Inclusion Criteria: 1. Patients will sign the informed consent form before the initiation of any study procedure. 2. Males and Females, 18 years or older 3. Patients must have a FFPE tumor block, one representative hematoxylin and eosin (H\&E) and 20 unstained sarcoma/endometrial carcinoma tissue slides available for submission to pathology review; this step is mandatory prior to registration to confirm eligibility. 4. Tumors must immune-stain negatively to one or more of the following proteins: MLH1, MSH2, MSH6 and PMS2 5. Patients must have histologically confirmed bone or soft tissue sarcoma by pathology review or a diagnosis of FIGO grade 3 endometrioid cancer, serous, clear cell, or mixed high grade endometrial cancer. 6. Measurable disease of sarcoma or endometrial carcinoma defined as lesions that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>10 mm with CT scan or MRI, as \>20 mm by chest x-ray, or \>10 mm with calipers by clinical exam by RECIST 1.1. 7. Locally advanced non-operable or metastatic disease 8. \>= 1 prior systemic therapy for sarcoma or endometrial carcinoma, including adjuvant systemic therapy 9. No treatment with biologic therapy, immunotherapy, chemotherapy, investigational agent for malignancy =\< 21 days before study registration 10. Eastern Cooperative Oncology Group ECOG performance status 0 or 1 11. Screening laboratory values must meet the following criteria and should be obtained within 14 days prior to first drug dose * WBC ≥ 2000/μL * Neutrophils ≥ 1500/μL * Platelets ≥ 100 x103/μL * Hemoglobin \> 9.0 g/dL * Serum creatinine ≤ 1.5 x ULN or creatinine clearance (CrCl) ≥ 40 mL/min (if 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 x 1.00 72 x serum creatinine in mg/dL * AST/ALT ≤ 3 x ULN * Total Bilirubin ≤ 1.5 x ULN (except subjects with Gilbert Syndrome, who can have total bilirubin \< 3.0 mg/dL) * Serum electrolytes: baseline serum potassium \> 3.5 mmol/L (potassium supplementation may be given to restore the serum potassium above this level prior to study entry) * Thyroid stimulating hormone (TSH) within normal limits (WNL); supplementation is acceptable to achieve a TSH WNL; in patients with abnormal TSH if free T4 is normal and patient is clinically euthyroid, patient is eligible 12. Patients should have resolution of any toxic effects of prior therapy (except alopecia) to NCI CTCAE, version 4.0, grade 1 or less 13. Patients may be re-screened and re-enrolled in the study if they failed screening or were enrolled but did not receive study drugs in this case they will have to sign a new informed concent form. 14. Palliative (limited-field) radiation therapy is permitted, if all of the following criteria are met: * Repeat imaging demonstrates no new sites of bone metastases. * The lesion being considered for palliative radiation is not a target lesion. 15. A negative pregnancy test (a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG)) done =\< 7 days prior to the start of study drug. 16. Women of childbearing potential (WOCBP) must use appropriate method(s) of contraception. WOCBP should use an adequate method to avoid pregnancy for 5 months (30 days plus the time required for nivolumab to undergo five half-lives) after the last dose of investigational drug 17. Women of childbearing potential must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 24 hours prior to the start of nivolumab 18. Women must not be breastfeeding 19. Men who are sexually active with WOCBP must use any contraceptive method with a failure rate of less than 1% per year. Men receiving nivolumab and who are sexually active with WOCBP will be instructed to adhere to contraception for a period of 7 months after the last dose of investigational product Women who are not of childbearing potential (ie, who are postmenopausal or surgically sterile as well as azoospermic men do not require contraception Exclusion Criteria: 1. Active, known or suspected autoimmune disease. Subjects 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 2. 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. 3. FIGO grade 1 or 2 endometrioid cancer. 4. Have had prior treatment with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CTLA-4 antibody, or any other antibody or drug specifically targeting T-cell costimulation or immune checkpoint pathways 5. Prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to the first dose of nivolumab/ipilimumab or has not recovered (i.e., to ≤ grade 1 or baseline) from adverse events due to a previously administered agent. Note, subjects with ≤ grade 2 neuropathy are an exception to this criterion and may qualify for the study. Note, if a subject received major surgery, she must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy. 6. No known or suspected allergy to nivolumab or study drug components and no history of severe hypersensitivity reaction to any monoclonal antibody 7. Active brain metastases or leptomeningeal metastases. Subjects with brain metastases are eligible if metastases have been treated and there is no magnetic resonance imaging (MRI) evidence of progression for at least 4 weeks after treatment is complete and within 28 days prior to the first dose of nivolumab administration. 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. 8. As there is potential for hepatic toxicity with nivolumab or nivolumab/ipilimumab combinations, drugs with a predisposition to hepatoxicity should be used with caution in patients treated with nivolumab-containing regimen. 9. 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 10. Have known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS) 11. Known active pulmonary disease with hypoxia defined as: Oxygen saturation \< 85% on room air or Oxygen saturation \< 88% despite supplemental oxygen 12. Pregnant and nursing women 13. Eastern Cooperative Oncology Group (ECOG) performance status 3-4 14. Prior malignancy active within the previous 3 years except for locally curable cancers that have been apparently cured, such as basal or squamous cell skin cancer, superficial bladder cancer, or carcinoma in situ of the prostate, cervix, or breast.