Leflunomide in Combination With Steroids for the Treatment of Acute Graft-versus-Host Disease After Donor Stem Cell Transplant for Hematologic Malignancies

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 * Age \>= 18 years old * Karnofsky performance status \>= 70 * Clinically suspected grade II-IV aGvHD based on Mount Sinai Acute GVHD International Consortium (MAGIC) Consensus criteria occurring after allogeneic hematopoietic cell transplantation (HCT) and GvHD prophylaxis regimen. Grade I acute (a)GvHD requiring systemic steroids is allowed. Clinical suspicion of aGvHD by the treating physician is sufficient, provided that alternative diagnosis of drug effects or infection are adequately ruled out * Note: HCT from any donor (related or unrelated with any degree of human leukocyte antigen \[HLA\] matching) and any graft source (bone marrow, peripheral blood stem cells, or cord blood) for hematologic malignancy or disorder. Recipient of myeloablative and reduced-intensity conditioning regimens are eligible * Biopsy of acute GvHD target organ is recommended but not required. Enrollment should not be delayed for biopsy or pathology results. Patients who do not enroll within 72 hours from start of steroids are not permitted to participate * Evidence of myeloid engraftment (e.g., absolute neutrophil count \[ANC\] \>= 0.5 x 10\^9/L for 3 consecutive days if ablative therapy was previously used). Use of growth factor supplementation is allowed * No prior systemic treatment for treatment of acute GvHD except for a maximum of 72 hours of prednisone =\< 2 mg/kg/day (or intravenous \[IV\] methylprednisone equivalent). Topical skin steroid treatment and non-absorbable oral steroid treatment for GI GvHD are permissible * Patients should be able to swallow and retain oral medication * Total bilirubin =\< 2 X ULN (unless has Gilbert's disease or aGvHD within 3 days of enrollment) (performed within 14 days prior to day 1 of protocol therapy) * Aspartate aminotransferase (AST) =\< 3 x upper limit of normal (ULN) (performed within 14 days prior to day 1 of protocol therapy) * Alanine aminotransferase (ALT) =\< 3 x ULN (performed within 14 days prior to day 1 of protocol therapy) * Creatinine clearance of \>= 50 mL/min per 24-hour urine test or the Cockcroft-Gault formula (performed within 14 days prior to day 1 of protocol therapy) * 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 3 months 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: * Recipient of more than one allogeneic HCT * Received more than 3 days of systemic corticosteroid for treatment of aGvHD * Presence of GVHD overlap syndrome * Prior treatment with leflunomide * Current or planned use of other investigational agents, or concurrent biological, chemotherapy, or radiation therapy during the study treatment period * Use of other drugs for treatment of acute GvHD * History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agent (leflunomide or cholestyramine) * Clinically significant uncontrolled illness * Patients on dialysis * Patient requiring ventilator support * Presence of an active uncontrolled infection. 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 * Known history of immunodeficiency virus (HIV) infection * Active hepatitis B virus (HBV) or hepatitis C virus (HCV) infection that requires treatment, HBV deoxyribonucleic acid (DNA) and HCV ribonucleic acid (RNA) must be undetectable upon testing. Prior test results obtained as part of standard of care that confirm a subject is immune and not at risk for reactivation (i.e., hepatitis B surface antigen negative, surface antibody positive) may be used for purpose of eligibility and test do not need to be repeated. Subjects within prior positive serology results must have negative polymerase chain reaction results. Subjects whose immune status is unknown must have results confirming immune status before enrolment * Subjects with evidence of relapsed primary disease, or subjects who have been treated for relapse after the allogeneic (allo)-HCT was performed * Severe organ dysfunction unrelated to underlying GvHD, including: * Cholestatic disorders or unresolved veno-occlusive disease of the liver (defined as persistent bilirubin abnormalities not attributable to GvHD and ongoing organ dysfunction) * Clinically significant uncontrolled cardiac disease, including unstable angina, acute myocardial infarction within 6 months of enrollment, New York Heart Association Class III or IV congestive heart failure, circulatory collapse requiring vasopressor or inotropic support, or arrhythmia that requires therapy * Clinically significant respiratory disease that requires mechanical ventilation support or 50% oxygen * 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 * Females only: Pregnant or