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 pro…