Testing Nivolumab With or Without Ipilimumab in Deficient Mismatch Repair System (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 mm or pathological lymph nodes with \>= 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 =\<3 x ULN may be enrolled) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 3 x ULN * Adequate oxygen saturation via pulse oximeter (CTCAE v.5.0 hypoxia \< grade 2 within 28 days prior to registration) * Thyroid-stimulating hormone (TSH) within normal limits (TSH \< ULN allowed in euthyroid patients on thyroid replacement therapy). TSH testing is only required if clinically indicated * Patients must have recovered from effects of recent surgery, radiotherapy or chemotherapy. At least 4 weeks must have elapsed since major surgery * As clinically indicated, patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better and have a corrected QT (QTc) interval \< 450 msec * The effects of nivolumab, and ipilimumab on the developing human fetus are unknown. For this reason and because nivolumab and ipilimumab are known to be teratogenic, women of child-bearing potential (WOCBP) must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for 5 months after the last dose of investigational drug. Women of childbearing potential must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin \[HCG\]) within 24 hours prior to the start of nivolumab. Women must not be breastfeeding. Women who are not of childbearing potential (i.e., who are postmenopausal or surgically sterile) do not require contraception * 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 postmenopau