Leflunomide, Pomalidomide, and Dexamethasone for the Treatment of Relapsed or Refractory Multiple Myeloma

Inclusion Criteria:

* Documented informed consent of the participant and/or legally authorized representative

  * Assent, when appropriate, will be obtained per institutional guidelines
* Agreement to allow the use of archival tissue from diagnostic tumor biopsies

  * If unavailable, exceptions may be granted with study principal investigator (PI) approval
* Eastern Cooperative Oncology Group (ECOG) =\< 2
* Life expectancy \> 3 months
* Diagnosis of multiple myeloma with measurable disease as defined by:

  * M-protein quantities \>= 0.5 g/dL by serum protein electrophoresis (sPEP) or
  * \>= 200 mg/24 hour urine collection by urine protein electrophoresis (uPEP) or
  * Serum free light chain (FLC) \> 10.0 mg/dL involved light chain and an abnormal kappa/lambda ration in subjects without detectable serum or urine M-protein or
  * For subjects with immunoglobulin class A (IgA) myeloma whose disease can only be reliably measured by quantitative immunoglobulin measurement, a serum IgA level \>= 0.50 g/dL
* Relapsed or refractory to at least 1 prior line of therapy, including both a proteasome inhibitor and an immunomodulatory drug, and for whom transplant is not recommended. Participants may opt for a delayed transplant at a later time, if appropriate
* Fully recovered from the acute toxic effects (except alopecia) to =\< grade 2 to prior anti-cancer therapy
* Absolute neutrophil count (ANC) \>= 1.0 x 10\^9/L (performed within 30 days prior to day 1 of protocol therapy unless otherwise stated)

  * NOTE: Screening ANC should be independent of granulocyte- and granulocyte/macrophage colony stimulating factor (G-CSF and GM-CSF) support for at least 1 week and of pegylated G-CSF for at least 2 weeks
* Platelets \>= 75.0 x 10\^9/L (performed within 30 days prior to day 1 of protocol therapy unless otherwise stated)

  * NOTE: Screening platelet count should be independent of platelet transfusions for at least 2 weeks
* Hemoglobin \>= 8.0 g/dL (performed within 30 days prior to day 1 of protocol therapy unless otherwise stated)

  * NOTE: Transfusion support is allowed
* Total bilirubin =\< 2 X upper limit of normal (ULN) (unless has Gilbert's disease) (performed within 30 days prior to day 1 of protocol therapy unless otherwise stated)
* Aspartate aminotransferase (AST) =\< 3.5 x ULN (performed within 30 days prior to day 1 of protocol therapy unless otherwise stated)
* Alanine aminotransferase (ALT) =\< 3.5 x ULN (performed within 30 days prior to day 1 of protocol therapy unless otherwise stated)
* Alkaline phosphatase \< 5 x ULN (performed within 30 days prior to day 1 of protocol therapy unless otherwise stated)
* Creatinine clearance of \>= 30 mL/min per 24 hour urine test (performed within 30 days prior to day 1 of protocol therapy unless otherwise stated)
* Women of childbearing potential (WOCBP): negative urine or serum pregnancy test

  * If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required
* Agreement by females and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 4 weeks after the last dose of protocol therapy

  * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only)

Exclusion Criteria:

* Prior treatment with leflunomide
* Patients who are pomalidomide refractory, defined as subjects who progress on or within 60 days of pomalidomide when given as a single agent or in combinatorial therapies. Prior exposure to pomalidomide without refractoriness is allowed
* Current or planned use of other anti-myeloma therapies besides leflunomide, pomalidomide, and dexamethasone
* Current or planned growth factor or transfusion support until after initiation of treatment
* Prior allogeneic transplant
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agents
* Positive for tuberculosis or latent tuberculosis (TB)
* Positive for hepatitis A, B, or C
* Known human immunodeficiency virus (HIV) infection
* Prior diagnosis of rheumatoid arthritis
* Acute active infection requiring systemic therapy within 2 weeks prior to enrollment
* Subject has history of anaphylaxis to thalidomide, lenalidomide, pomalidomide, cholestyramine or dexamethasone
* Non-hematologic malignancies within the past 3 years, with the exceptions of

  * Adequately treated basal cell or squamous cell skin cancer,
  * Carcinoma in situ of the cervix,
  * Prostate cancer \< Gleason grade 6 with stable prostate specific antigen (PSA), or
  * Successfully treated in situ carcinoma of the breast
* Females only: Pregnant or breastfeeding
* Any other condition that would, in the Investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures
* 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)