Leflunomide in Treating Patients With Relapsed or Refractory Multiple Myeloma

Inclusion Criteria: * All subjects must have the ability to understand and the willingness to sign a written informed consent * Patients must have a life expectancy of \> 3 months * Patients must exhibit an Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 * Patients must have a diagnosis of multiple myeloma * Serum M-protein \>= 0.5 g/dL * Urine M-protein \>= 200 mg/24 hr * Serum free light chain \>=10 mg/dL provided the free light chain (FLC) ratio is abnormal * 10% plasma cells in bone marrow * Patients must be relapsed or are refractory to at least 3 prior lines of therapy, including both a proteasome inhibitor an immunomodulatory drug (IMiD), and for whom a transplant is not recommended (induction therapy and stem cell transplant +/- maintenance will be considered as one regimen) * At least 2 weeks from prior therapy to time of start of treatment; prior therapy includes steroids (except prednisone or equivalent - up to 10 mg per day is allowed) * Platelet count \>= 50,000/uL; platelet transfusions are not allowed within 14 days of platelet assessment * Absolute neutrophil count (ANC) \>= 1000/mm\^3; growth factor is not permitted within 14 days of neutrophil assessment * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.0 x upper limit of normal (ULN) * Total Bilirubin \< 1.5 x ULN * Calculated creatinine clearance (CrCl) \>= 30 mL/min per 24 hour urine collection or the Cockcroft-Gault formula * Negative serum or urine beta-human chorionic gonadotropin (B-HCG) test (female patient of childbearing potential\* only), to be performed locally within the screening period * Negative for tuberculosis antigen (e.g. T-Spot test) * Negative for hepatitis A, B, or C infection * Adequate pulmonary function as defined by forced vital capacity (FVC) and diffusing capacity of the lung for carbon monoxide (DLCO) \>= 50% of predicted by pulmonary function testing * Agreement by females of childbearing potential\* and sexually active males to use an effective method of contraception (hormonal or barrier method of birth control or abstinence) prior to study entry and for three months following duration of study participation; should a woman become pregnant or suspect that she is pregnant while participating on the trial, she should inform her treating physician immediately \* A female of childbearing potential is defined as a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months Exclusion Criteria: * Prior treatment with leflunomide * Current or planned use of other investigational agents, or concurrent biological, chemotherapy, or radiation therapy during the study treatment period * Current or planned growth factor or transfusion support until after initiation of treatment; if growth factor or transfusion support is provided between screening and start of treatment, the participant will no longer be eligible * Prior diagnosis of rheumatoid arthritis * Prior allogenic transplant * Acute active infection requiring systemic therapy within 2 weeks prior to enrollment * Pre-existing liver disease * Known human immunodeficiency virus (HIV) infection * History of allergic reactions attributed to compounds of similar chemical or biologic composition to leflunomide or cholestyramine * Non-hematologic malignancy within the past 3 years aside from the following exceptions: * Adequately treated basal cell or squamous cell skin cancer * Carcinoma in situ of the cervix * Prostate cancer \< Gleason grade 6 with a stable prostate specific antigen (PSA) * Successfully treated in situ carcinoma of the breast * Clinically significant medical disease or condition that, in the investigator's opinion, may interfere with protocol adherence or the patient's ability to give informed consent * Pregnant women and women who are lactating; breastfeeding should be discontinued if the mother is enrolled on this study * Any other condition that would, in the investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns or compliance with clinical study procedures, e.g., infection/inflammation, intestinal obstruction, unable to swallow medication, social/ psychological issues, etc * NONCOMPLIANCE: Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)