Romidepsin in Treating Patients With Steroid-Refractory Graft-versus-Host Disease

Inclusion Criteria: * Patients with steroid (or immunosuppressive therapy \[IST\]) refractory acute GVHD (aGVHD) or chronic GVHD (cGVHD) * Absolute neutrophil count \>= 750/mm\^3 * Platelet count \>= 50,000/mm\^3 * Corrected QT interval (QTc) =\< 480 msec * Bilirubin =\< 1.5 x upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x ULN * Serum potassium \>= 3.8 mmol/L * Serum magnesium \>= 1.8 mg/dL * Serum creatinine =\< 2.0 mg/dl * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-3 * Patients may undergo electrolyte repletion therapy to meet eligibility requirements * Patients must be scheduled for tapering doses of (or no longer treated with): * Cyclosporine; * Tacrolimus; * Sirolimus; * Steroids (patients may be on physiologic doses of steroids) * Patients receiving extracorporeal photopheresis must discontinue extracorporeal photopheresis or placed on a tapering schedule; * Any prior therapy for GVHD must be completed and discontinued with the exception of the above; * Patients with breakpoint cluster region (bcr)-ABL proto-oncogene 1 (abl) associated malignancies may be on a tyrosine kinase inhibitor as malignant disease therapy or prophylaxis * There must be no uncontrolled active infections or medical conditions that the investigator feels will compromise the safety of the treatment and/or the assessment of the efficacy of therapy * The patient must be aware of the high risk and experimental nature of the treatment and provide informed consent * Negative serum pregnancy test at the time of enrollment for females of childbearing potential * For males and females of child-producing potential, use of effective contraceptive methods during the study and for at least 6 months after the last dose of romidepsin Exclusion Criteria: * Active/uncontrolled infection * Evidence of relapsed disease * Life expectancy \< 12 weeks * Pregnant or breast feeding females * Prior therapy with romidepsin * Known seropositive for or active viral infection with human immunodeficiency virus (HIV), hepatitis B virus (HBV) or hepatitis C virus (HCV); patients who are seropositive because of hepatitis B virus vaccine are eligible * Any known cardiac abnormalities such as: * Congenital long QT syndrome * QTc interval \>= 480 milliseconds; * Myocardial infarction within 6 months of course 1, day 1 (C1D1); subjects with a history of myocardial infarction between 6 and 12 months prior to C1D1 who are asymptomatic and have had a negative cardiac risk assessment (treadmill stress test, nuclear medicine stress test, or stress echocardiogram) since the event may participate; * Other significant electrocardiogram (ECG) abnormalities including 2nd degree atrio-ventricular (AV) block type II, 3rd degree AV block, or bradycardia (ventricular rate less than 50 beats/min); * Symptomatic coronary artery disease (CAD), e.g., angina Canadian class II-IV; in any patient in whom there is doubt, the patient should have a stress imaging study and, if abnormal, angiography to define whether or not CAD is present; * An ECG recorded at screening showing evidence of cardiac ischemia (ST depression of \>= 2 mm, measured from isoelectric line to the ST segment); if in any doubt, the patient should have a stress imaging study and, if abnormal, angiography to define whether or not CAD is present; * Congestive heart failure (CHF) that meets New York Heart Association (NYHA) class II to IV definitions and/or ejection fraction \< 40% by multi gated acquisition (MUGA) scan or \< 50% by echocardiogram and/or magnetic resonance imaging (MRI); * A known history of sustained ventricular tachycardia (VT), ventricular fibrillation (VF), Torsade de Pointes, or cardiac arrest unless currently addressed with an automatic implantable cardioverter defibrillator (AICD); * Hypertrophic cardiomegaly or restrictive cardiomyopathy from prior treatment or other cause; * Any cardiac arrhythmia requiring an anti-arrhythmic medication (excluding stable doses of beta-blockers) * Uncontrolled hypertension, i.e., blood pressure (BP) of \>= 160/95; patients who have a history of hypertension controlled by medication must be on a stable dose (for at least one month) and meet all other inclusion criteria; or * Patients taking drugs leading to significant QT prolongation must have an ECG prior to each treatment * Concomitant use of cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) inhibitors * Concomitant use of medications known to induce a disulfiram-like reaction to alcohol