Ibrutinib and Nivolumab in Treating Patients With Previously-Treated Metastatic Kidney Cancer

Inclusion Criteria: * Metastatic renal cell cancer patients (any histologic subtype) with measurable and/or evaluable disease who have completed at least one line of prior systemic therapy are potentially eligible for this trial; any number of prior systemic therapies are allowed, including prior nivolumab * Absolute neutrophil count \> 750 cells/mm\^3 (0.75 x 10\^9/L) * Platelet count \> 50,000 cells/mm\^3 (50 x 10\^9/L) * Hemoglobin \> 8.0 g/dL * Serum aspartate transaminase (aspartate aminotransferase \[AST\]) or alanine transaminase (alanine aminotransferase \[ALT\]) =\< 3.0 x upper limit of normal (ULN) * Estimated creatinine clearance \>= 30 ml/min (Cockcroft-Gault) * Bilirubin =\< 1.5 x ULN (unless bilirubin rise is due to Gilbert's syndrome or of non-hepatic origin) * Prothrombin time (PT)/international normalized ratio (INR) \< 1.5 x ULN and partial thromboplastin time (PTT) (activated partial thromboplastin time \[aPTT\]) \< 1.5 x ULN * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 * Female subjects who are of non-reproductive potential (i.e., post-menopausal by history - no menses for \>= 1 year; OR history of hysterectomy; OR history of bilateral tubal ligation; OR history of bilateral oophorectomy); female subjects of childbearing potential must have a negative serum pregnancy test upon study entry * Male and female subjects who agree to use both a highly effective methods of birth control (e.g., implants, injectables, combined oral contraceptives, some intrauterine devices \[IUDs\], sexual abstinence, or sterilized partner) and a barrier method (e.g., condoms, cervical ring, sponge, etc.) during the period of therapy and for 30 days after the last dose of study drug Exclusion Criteria: * Cytotoxic chemotherapy =\< 21 days prior to first administration of study treatment and/or monoclonal antibody =\< 4 weeks prior to first administration of study treatment and/or other renal cell carcinoma (RCC)-directed systemic therapy =\< 2 weeks prior to first administration of study treatment * History of other malignancies, except: * Malignancy treated with curative intent and with no known active disease present for \>= 3 years before the first dose of study drug and felt to be at low risk for recurrence by treating physician * Adequately treated non-melanoma skin cancer or lentigo malignancy without evidence of disease * Adequately treated carcinoma in situ or T1 urothelial cancer without evidence of disease * Concurrent systemic immunosuppressant therapy (e.g., cyclosporine A, tacrolimus, etc., or chronic administration \[\> 14 days\] of \> 10 mg/day of prednisone) within 28 days of the first dose of study drug * Vaccinated with live, attenuated vaccines within 4 weeks of first dose of study drug * Recent infection requiring systemic treatment that was completed =\< 14 days before the first dose of study drug * Unresolved toxicities from prior anti-cancer therapy, defined as having not resolved to Common Terminology Criteria for Adverse Event (CTCAE, version 4), grade =\< 1, or to the levels dictated in the inclusion/exclusion criteria with the exception of alopecia * Known bleeding disorders (e.g., von Willebrand's disease) or hemophilia * History of stroke or intracranial hemorrhage within 6 months prior to enrollment * Known history of human immunodeficiency virus (HIV) or active with hepatitis C virus (HCV) or hepatitis B virus (HBV); subjects who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded * Any uncontrolled active systemic infection * Major surgery within 4 weeks of first dose of study drug * Any life-threatening illness, known autoimmune disease, medical condition, or organ system dysfunction that, in the investigator's opinion, could compromise the subject's safety or put the study outcomes at undue risk * Currently active, clinically significant cardiovascular disease, such as uncontrolled arrhythmia or class 3 or 4 congestive heart failure as defined by the New York Heart Association Functional Classification; or a history of myocardial infarction, unstable angina, or acute coronary syndrome within 6 months prior to enrollment * Unable to swallow capsules or malabsorption syndrome, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel, symptomatic inflammatory bowel disease or ulcerative colitis, or partial or complete bowel obstruction * Lactating or pregnant * Unwilling or unable to participate in all required study evaluations and procedures * Unable to understand the purpose and risks of the study and to provide a signed and dated informed consent form (ICF) and authorization to use protected health information (in accordance with national and local subject privacy regulations) * Concomitant use of warfarin or other vitamin K antagonists; Note: Subjects receiving antiplatelet agents in conjunction with ibrutinib should be observed closely for any signs of bleeding or bruising, and ibrutinib should be withheld in the event of any bleeding events; supplements such as fish oil and vitamin E preparations should be avoided * Requires treatment with a strong cytochrome P450 (CYP) 3A4/5 inhibitor * QT prolongation and/or familiar history of QT prolongation and uncontrolled cardiac arrhythmias * Currently active, clinically significant hepatic impairment Child-Pugh class B or C according to the Child Pugh classification