Lenalidomide and Nivolumab in Treating Patients With Relapsed or Refractory Multiple Myeloma

Inclusion Criteria: * Patients with evidence of relapse or refractory disease as defined by International Myeloma Working Group (IMWG) criteria and measurable disease as defined by any of the following: * Serum m-protein \>= 0.5 g/dl (\>= 10 g/l) * Urine monoclonal protein \>= 200 mg/24 hour(h) * Involved free light chain (FLC) level \>= 10mg/dl (\>= 100mg/l) and an abnormal serum free light chain ratio (\< 0.26, or \> 1.65) * Measurable biopsy proven plasmacytoma (should be measured within 28 days of initial investigational agent dosing) * Patients must have had at least 2 prior line of therapy * Patients must not have had progression of disease on lenalidomide 25 mg; stable disease on lenalidomide is permitted * Patient may be enrolled at any time from last line of therapy * Patients must have absolute neutrophil count (ANC) \> 1000/uL * Platelets \>= 75,000/uL, if plasma cell percentage on bone marrow biopsy aspirate or core is \> 30%, platelet eligibility requirement will be adjusted to 60,000/ul * Total bilirubin =\< 1.5 mg/dL * Alkaline phosphatase =\< 3 X the upper limit of normal (ULN) * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2 X the ULN * Patients must have adequate renal function as evidenced by serum creatinine =\< 2 mg/dL or calculated creatinine clearance of \>= 40 ml/min within 14 days of registration using Modification of Diet in Renal Disease (MDRD) formula * Patient must be able to swallow capsule or tablet * Patients must provide informed consent * Patients must have a left ventricular ejection fraction \> 30%, no uncontrolled arrhythmias or New York Heart Association class III-IV heart failure * Patients must have a Karnofsky performance status \>= 70 * A negative pregnancy test will be required for all women of child bearing potential; breast feeding is not permitted * Fertility requirements * Female patients with child bearing potential must have a negative pregnancy test at least 7 days before starting treatment drugs * Male patients must agree to use an adequate method of contraception for the duration of the study and for 7 months afterwards * Female patients must be either posy-menopausal, free from menses \>= 2 years (yrs), surgically sterilized, willing to use two adequate barrier methods of contraception to prevent pregnancy, or agree to abstain from sexual activity starting from screening and for 5 months afterwards * Female patients of child bearing potential must agree to comply with the fertility and pregnancy test requirements dictated by the Rev-Assist program Exclusion Criteria: * Patients with peripheral neuropathy \> Common Terminology Criteria for Adverse Events (CTCAE) grade 2 * Patients receiving concurrent corticosteroids at the time protocol therapy is initiated other than for physiologic maintenance treatment * History of allergic reaction (including erythema nodosum) to lenalidomide * Concurrent use of complementary or alternative medicines that would confound the interpretation of toxicities and antitumor activity of the study drugs * Patients with contraindication to thromboprophylaxis * Unacceptable cardiac risk factors defined by any of the following criteria: patients with congenital long QT syndrome, any history of ventricular fibrillation or torsade de pointes, bradycardia defined as heart rate (HR) \< 50 bpm, left ventricular ejection fraction \< 30% * Patients who have received targeted or investigational agents within 2 weeks or within 5 half-lives of the agent and active metabolites (whichever is longer) and who have not recovered from side effects of those therapies * Patients who have undergone major surgery =\< 2 weeks prior to starting study drug or who have not recovered from the side-effects of surgery * Patients with known positivity for human immunodeficiency virus (HIV), or hepatitis C; baseline testing for HIV and hepatitis C is not required * Patients with a history of another primary malignancy that is currently clinically significant or currently requires active intervention, other than non-melanoma skin cancer and carcinoma in situ of the cervix should not be enrolled; patients are not considered to have a ?currently active? malignancy if they have completed therapy for a prior malignancy, are disease free from a prior malignancy for \>= 5 yrs and are considered by their physician to be less than 30% risk of relapse * Patients with active (untreated or relapsed) central nervous system (CNS) metastasis of the patient?s myeloma * Patients with a history of gastrointestinal surgery or other procedure that might, in the opinion of the investigator(s), interfere with the absorption or swallowing of the study drugs * Patients with any significant history of non-compliance to medical regimens or unwilling or unable to comply with the instructions given to them by the study staff * Any other medical condition, including mental illness or substance abuse, deemed by the investigator(s) to likely interfere with the patient?s ability to sign informed consent, cooperate and participate in the study, or interfere with the interpretation of the results