Testing Nivolumab With or Without Ipilimumab in Deficient Mismatch Repair System (dMMR) Recurrent Endometrial Carcinoma

This phase II trial tests whether the combination of nivolumab and ipilimumab is better than nivolumab alone to shrink tumors in patients with deficient mismatch repair system (dMMR) endometrial carcinoma that has come back after a period of time during which the cancer could not be detected (recurrent). Deoxyribonucleic acid (DNA) mismatch repair (MMR) is a system for recognizing and repairing damaged DNA. In 2-3% of endometrial cancers this may be due to a hereditary condition resulted from gene mutation called Lynch Syndrome (previously called hereditary nonpolyposis colorectal cancer or HNPCC). MMR deficient cells usually have many DNA mutations. Tumors that have evidence of mismatch repair deficiency tend to be more sensitive to immunotherapy. There is some evidence that nivolumab with ipilimumab can shrink or stabilize cancers with deficient mismatch repair system. However, it is not known whether this will happen in endometrial cancer; therefore, this study is designed to answer that question. Monoclonal antibodies, such as nivolumab and ipilimumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Giving nivolumab in combination with ipilimumab may be better than nivolumab alone in treating dMMR recurrent endometrial carcinoma.

Inclusion Criteria: * Patients with measurable or non-measurable (detectable) recurrent endometrial cancer * Measurable disease will be defined and monitored by RECIST v 1.1. Measurable disease is defined per RECIST 1.1 criteria as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded). Each lesion must be \>= 10 mm when measured by computed tomography (CT) or magnetic resonance imaging (MRI). Lymph nodes must be \>= 15 mm in short axis when measured by CT or MRI * Non-measurable (detectable) disease in a patient is defined in this protocol per RECIST 1.1 criteria as one who does not have measurable disease but has at least one of the following conditions: * All other lesions (or sites of disease), including small lesions (longest diameter \= 10 to \< 15 mm short axis), are considered non-measurable disease * Ascites and/or pleural effusion attributed to tumor * Solid and/or cystic abnormalities on radiographic imaging that do not meet RECIST 1.1 definitions for target lesions * Patients must have endometrial cancer with deficient mismatch repair system. All patients must have institutional immunohistochemistry (IHC) and/or microsatellite instability (MSI) testing to determine mismatch repair (MMR) status. MMR deficiency is defined as lack of expression of one or more mismatch repair proteins (MLH1, PMS2, MSH2, MSH6, EPCAM) by immunohistochemistry and/or presence of microsatellite instability high using the National Cancer Institute (NCI)-5plex and Promega v1.2 assays, or institutional standards (e.g. next-generation sequencing \[NGS\] panel) * Method(s) of detection of MMR deficiency will be recorded for each patient. An institutional pathology report, and additional reports if available, documenting these results must be submitted. Patients with "equivocal" results on MMR testing by immunohistochemistry may be eligible if they have documented evidence of microsatellite instability by MSI testing or by next generation sequencing assays. MMR testing by IHC may be used to resolve equivocal/indeterminate MSI results * Histologic confirmation of the original primary tumor is required (submission of pathology report(s) is required). Patients with the following histologic types are eligible: Endometrioid adenocarcinoma, mucinous adenocarcinoma, dedifferentiated/undifferentiated carcinoma, clear cell adenocarcinoma, mixed epithelial carcinoma, adenocarcinoma not otherwise specified (N.O.S.) * Patients may have received 1-2 prior lines of systemic therapy: * Prior anti-PD1/PD-L1 therapy is allowed if given in combination with chemotherapy or radiation therapy in adjuvant or primary metastatic/recurrent settings. Patients must have had a complete response and have disease progression/relapse with treatment-free interval of 12 months or more from last dose of therapy with immune check inhibition * Patients may have received prior radiation therapy for treatment of endometrial cancer. Prior radiation therapy may have included pelvic radiation therapy, extended field pelvic/para aortic radiation therapy, intravaginal brachytherapy, and/or palliative radiation therapy. All radiation therapy must be completed at least 4 weeks prior to registration * Patients may have received prior hormonal therapy for treatment of endometrial cancer. All hormonal therapy must be discontinued at least three weeks prior to registration * Any other prior therapy directed at the malignant tumor including chemotherapy, targeted agents, biologic agents, immunologic agents, and any investigational agents, must be discontinued at least 4 weeks prior to registration (6 weeks for nitrosoureas or mitomycin C) * Age \>= 18 * Eastern Cooperative Oncology Group (ECOG) Performance Status of 0, 1, or 2 * Platelets \>= 100,000/mcl * Absolute neutrophil count (ANC) \>= 1,500/mcl * Creatinine =\< 1.5 x institutional/laboratory upper limit of normal (ULN) * Total serum bilirubin level =\< 1.5 x ULN (patients with known Gilbert's disease who have bilirubin level =\