Testing the Investigational Medication Pembrolizumab After Kidney Removal for Patients With Non-Clear Cell Renal Cell Carcinoma

Inclusion Criteria: * Patient must be ≥ 18 years of age * Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 * Patient must have histologically confirmed non-clear cell renal cell carcinoma (nccRCC) with ≥ pT3Nx or pTanyN+ or pTanyNanyM1 with no evidence of disease (NED) per the American Joint Committee on Cancer (AJCC) 8th edition * Patient must not have renal medullary carcinoma * Patient must have had a partial or radical nephrectomy. In the case of patients with M1 NED status, a complete resection of the metastatic lesion(s) (metastasectomy) must have been completed at the time of nephrectomy or within 1 year after nephrectomy * Positive margins are allowed as long as no gross disease * Patient must not have residual thrombus post nephrectomy in the vena renalis or vena cava * Patient must be randomized ≤ 16 weeks after nephrectomy and/or \< 16 weeks after metastasectomy * Patient must have undergone imaging of chest, abdomen and pelvis with a CT or MRI after nephrectomy/metastasectomy and within 42 days prior to randomization documenting there is no evidence of liver, bone, or brain metastases * Patient must not have received any prior anti-PD-1/PD-L1 or CTLA-4 agents * Patient must not have received any prior radiotherapy for nccRCC * Patient must not have received prior systemic treatment for nccRCC (except nephrectomy or metastasectomy). Patient must not have received prior immune checkpoint inhibitor agents for other cancers within 2 years prior to randomization * Patient must not have active known or suspected autoimmune disease requiring systemic immunosuppression. The following autoimmune disorders are permitted: patients with vitiligo, type I diabetes mellitus, controlled/stable hypo or hyperthyroidism due to autoimmune or non-autoimmune conditions (hormone replacement is allowed), psoriasis not requiring systemic treatment * Patient must not be on any immunosuppressant therapy other than inhaled steroids, intranasal steroids, topical steroids, injection steroids and systemic steroids up to 10mg prednisone equivalent * Patient must have recovered adequately from toxicity and/or complications related to any surgery received prior to randomization * Patient must not have a history or current evidence of uncontrolled intercurrent illness that would limit compliance with study requirement, substantially increase the risk of incurring adverse events (AEs), or compromise the ability of the patient to give written informed consent * Patient must not have had a history of allogeneic organ transplantation * Patient must not be pregnant or breast-feeding due to the potential harm to an unborn fetus and possible risk for adverse events in nursing infants with the treatment regimens being used * All patients of childbearing potential must have a blood test or urine study within 14 days prior to randomization to rule out pregnancy * A patient of childbearing potential is defined as anyone, regardless of whether they have undergone tubal ligation, who meets the following criteria: 1) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy; or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months) * Patient must not expect to conceive or father children by using accepted and effective method(s) of contraception or by abstaining from sexual intercourse for the duration of their participation in the study. Patients of childbearing potential assigned to Arm B must continue contraception requirements for 4 months following the last dose of pembrolizumab. Patients assigned to Arm B must also not breastfeed while on protocol treatment and for 4 months after the last dose of pembrolizumab * Patient must have the ability to understand and the willingness to sign a written informed consent document. Patients with impaired decision-making capacity (IDMC) who have a legally authorized representative (LAR) or caregiver and/or family member available will also be considered eligible * Leukocytes ≥ 3,000/ mm\^3 (must be obtained ≤ 42 days prior to protocol randomization) * Absolute neutrophil count (ANC) ≥ 1,500/mm\^3 (must be obtained ≤ 42 days prior to protocol randomization) * Platelets ≥ 100,000/ mm\^3 (must be obtained ≤ 42 days prior to protocol randomization) * Total bilirubin ≤ 2 x institutional upper limit of normal (ULN) (must be obtained ≤ 42 days prior to protocol randomization) * NOTE: For patients with known Gilbert's syndrome, total bilirubin \< 3 x ULN * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) ≤ 3.0 × institutional ULN (must be obtained ≤ 42 days prior to protocol randomization) * Estimated glomerular filtration rate (eGFR) clearance ≥ 30 mL/min/1.73 m\^2 (must be obtained ≤ 42 days prior to protocol randomization) * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months of randomization are eligible for this trial * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated * Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * 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 must be class 2 or better