Entinostat in Combination With Aldesleukin in Treating Patients With Metastatic Kidney Cancer

Inclusion Criteria: * Patients must have pathological diagnosis of renal cell carcinoma that is metastatic or surgically unresectable; the histology must be clear cell carcinoma or predominant clear cell carcinoma * Patients may have received up to two prior therapies including vascular endothelial growth factor (VEGF), mammalian target of rapamycin (mTOR) and programmed cell death (PD)-1/PD ligand 1 (L1) inhibitors; prior palliative radiation to metastatic lesion(s) is permitted, provided there is at least one measurable and/or evaluable lesion(s) that has not been irradiated * Patients must have measurable or evaluable disease * Eastern Cooperative Oncology Group (ECOG) performance status 0 * Life expectancy of greater than 6 months * Hemoglobin \>= 12 g/dL * Leukocytes \>= 3,000/mm\^3 * Absolute neutrophil count \>= 1,500/mm\^3 * Platelets \>= 100,000/mm\^3 * Total bilirubin =\< 1.5 x laboratory upper limit of normal * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x laboratory upper limit of normal * Creatinine =\< 1.5 x laboratory upper limit of normal or calculated creatinine clearance of \>= 50 ml/min * Lactate dehydrogenase (LDH) within normal limits (WNL) * Corrected calcium =\< 10 mg/dL * Prothrombin time (PT)/international normalized ratio (INR) =\< 1.5 * Urine protein \< 1+; if \>= 1+, 24 hour urine protein should be obtained and should be \< 1000 mg * Forced expiratory volume in 1 second (FEV1) \>= 2.0 liters or \>= 75% of predicted for height and age; (pulmonary function tests \[PFTs\] are required for patients over 50 or with significant pulmonary or smoking history) * No evidence of congestive heart failure, symptoms of coronary artery disease, myocardial infarction less than 6 months prior to entry, serious cardiac arrhythmias, or unstable angina; patients who are over 40 or have had previous myocardial infarction greater than 6 months prior to entry will be required to have a negative or low probability cardiac stress test for cardiac ischemia * No history of cerebrovascular accident or transient ischemic attacks * The effects of entinostat on the developing human fetus at the recommended therapeutic dose are unknown; for this reason Women of child-bearing potential 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; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately; men with female partners of child bearing potential must also agree to use adequate contraception * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have received more than two prior therapies * Concurrent use of valproic acid is not allowed * Patients may not be receiving any other investigational agents * Patients with untreated central nervous system (CNS) metastases; patients should have a head CT/magnetic resonance imaging (MRI) within 28 days prior to treatment initiation; patients with previously excised/gamma knifed solitary or oligometastases and controlled disease are eligible * Any medical condition that would preclude adequate evaluation of the safety and toxicity of the study combination * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure (New York Association class II, III, or IV), angina pectoris requiring nitrate therapy, recent myocardial infarction (\< the last 6 months), cardiac arrhythmia, history of cerebrovascular accident (CVA) within 6 months, hypertension (defined as blood pressure of \> 160 mmHg systolic and/or \> 90 mmHg diastolic on medication) history of peripheral vascular disease, or psychiatric illness/social situations that would limit compliance with study requirements * Patients with a history of allergy to entinostat or other medications that have a benzamide structure (i.e. tiapride, remoxipride, and clebopride) * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with entinostat * Human immunodeficiency virus (HIV)-positive patients receiving combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with entinostat. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy; appropriate studies will be undertaken in patients receiving combination anti-retroviral therapy when indicated * Serious or non-healing wound, ulcer or bone fracture * Major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to day 1 therapy * Anticipation of need for major surgical procedures during the course of the study * Left ventricular ejection function \< 45%