Leflunomide in Treating Patients With Steroid Dependent Chronic Graft Versus Host Disease

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. * Karnofsky performance status of \>= 70 %. * Ability to read and understand English or Spanish for questionnaires. * Recipients of allogeneic stem cell transplantation (sibling/unrelated/umbilical cord blood \[UCB\]/Haplo) with myeloablative or non-myeloablative conditioning regimens. * Participants must have steroid-dependent cGVHD. Steroid dependent cGVHD is defined as having persistent signs and symptoms of cGVHD despite the use of prednisone for 2 months without complete resolution of signs and symptoms. Both classic cGVHD and overlap syndromes will be allowed to participate. * Estimated life expectancy greater than 3 months. * No more than 4 prior lines of treatment. Sirolimus and tacrolimus used for prophylaxis will not be counted as line of therapy. * Stable dose of corticosteroids for 2 weeks prior to enrollment. * Able to swallow pills. * Absolute neutrophil count (ANC) \>= 1,000/mm\^3 (without myeloid growth factors within 1 week of study entry) (performed within 28 days prior to day 1 of protocol therapy unless otherwise stated). * Platelets \>= 50,000/mm\^3 (performed within 28 days prior to day 1 of protocol therapy unless otherwise stated). * NOTE: Platelet transfusions are not permitted within 14 days of platelet assessment unless cytopenia is secondary to disease involvement. * Total bilirubin =\< 2 mg/dl (exception permitted in patients with Gilbert's syndrome; aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2 x upper limit of normal \[ULN\]), unless hepatic dysfunction is a manifestation of presumed cGVHD (performed within 28 days prior to day 1 of protocol therapy unless otherwise stated). * Abnormal liver function tests (LFTs) (liver function panel) in the context of active cGVHD involving other organ systems may also be permitted if the treating physician documents the abnormal LFTs as being consistent with hepatic cGVHD and a liver biopsy will not be mandated in this situation. * AST =\< 2.0 x ULN (performed within 28 days prior to day 1 of protocol therapy unless otherwise stated). * ALT =\< 2.0 x ULN (performed within 28 days prior to day 1 of protocol therapy unless otherwise stated). * Creatinine clearance of \>= 60 mL/min/1.73 m\^2 for participants with creatinine levels above institutional normal. or calculated by Cockcroft-Gault equation (performed within 28 days prior to day 1 of protocol therapy unless otherwise stated). * Seronegative for human immunodeficiency virus (HIV) antigen (Ag)/antibody (Ab) combo, hepatitis C virus (HCV)\*, active hepatitis B virus (HBV) (surface antigen negative), and syphilis (rapid plasma reagin \[RPR\]) (performed within 28 days prior to day 1 of protocol therapy). * If positive, hepatitis C ribonucleic acid (RNA) quantitation must be performed. * Meets other institutional and federal requirements for infectious disease titer requirements (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated). * Note: Infectious disease testing to be performed within 28 days prior to day 1 of protocol therapy. * Women of childbearing potential (WOCBP): negative urine or serum pregnancy test (to be performed within 28 days prior to day 1 of protocol therapy unless otherwise stated). * 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 3 months after the last dose of protocol therapy. The effects of study treatment on a developing fetus have the potential for teratogenic or abortifacient effects. Should a woman become pregnant or suspect that she is pregnant while participating on the trial, she should inform her treating physician immediately. * 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: * Exposure to any new immunosuppressive medication in the 4 weeks prior to enrollment. * Donor lymphocyte infusion within 100 days prior to enrollment. * Patients may not be receiving any other investigational agents concurrently. Oral chemotherapeutic agents or biologics -for example ruxolitinib or rituximab therapy and ibrutinib / imatinib (either past or current exposure) - is allowed. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agent. * Active infection requiring antibiotics. An active uncontrolled infection is defined as hemodynamic instability attributed to sepsis or new symptoms, worsening physical signs, or radiographic findings attributable to infection. Persisting fever without signs or symptoms will not be interpreted as an active uncontrolled infection. * Uncontrolled cardiac angina or symptomatic congestive heart failure (New York Heart Association \[NYHA\] class III or IV). * Pregnant women are excluded from this study. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with leflunomide. * Patients should not have any uncontrolled illness including ongoing or active infection. * Active malignant relapse. * Patients with other active malignancies are ineligible for this study, other than superficial localized skin cancer (basal or squamous cell carcinoma). * Active diarrhea, not related to cGVHD. * Clinically significant uncontrolled illness. * Patients on dialysis. * Patients requiring ventilator support. * Patients with acute GvHD * Known history of immunodeficiency virus (HIV) or hepatitis B or hepatitis C infection. * 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. * Inability to comply with protocol therapy and follow up visits. * 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).