Depsipeptide (Romidepsin) in Treating Patients With Metastatic or Unresectable Soft Tissue Sarcoma

Inclusion Criteria: * Histologically or cytologically confirmed soft tissue sarcoma (STS), including, but not limited to, the following histologies: * Gastrointestinal stromal tumors (GIST) * Refractory to imatinib mesylate * Desmoplastic small round cell tumors * Clear cell sarcoma * Extraskeletal osteosarcoma\* * Extraskeletal Ewing's sarcoma\* * Extraskeletal (myxoid) chondrosarcoma\* * Secondary STS (e.g., radiation-induced STS or neurofibrosarcoma due to neurofibromatosis) allowed * Metastatic or unresectable disease * No standard curative therapy exists * Patients with GIST must have received and progressed on imatinib mesylate * Measurable disease, defined as ≥ 1 unidimensionally measurable lesion ≥ 20 mm by conventional techniques OR ≥ 10 mm by spiral CT scan * No known brain metastases * Performance status - Eastern Cooperative Oncology Group (ECOG) 0-2 * Performance status - Karnofsky 50-100% * More than 3 months * White blood cells (WBC) ⥠3,000/mm\^3 * Absolute neutrophil count ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ⤠2.5 times upper limit of normal (ULN) * Bilirubin normal * Creatinine \< 1.5 times ULN * Creatinine clearance ≥ 60 mL/min * QTc ≤ 480 msec Exclusion Criteria: * No cardiac abnormalities (e.g., congenital long QT syndrome) * No myocardial infarction within the past year * No history of coronary artery disease (e.g., angina Canadian Class II-IV or positive stress imaging study) * No cardiac ischemia (ST depression \>2 mm) by electrocardiogram (ECG) * No New York Heart Association Class II-IV congestive heart failure * Ejection fraction \> 50% by multi gated acquisition scan (MUGA) scan or echocardiogram * No history of sustained ventricular tachycardia, ventricular fibrillation, Torsades de Pointes, or cardiac arrest unless controlled by an automatic implantable cardioverter defibrillator * No hypertrophic or restrictive cardiomyopathy from prior treatment or other causes * No significant left ventricular hypertrophy * No uncontrolled hypertension (i.e., blood pressure ≥ 160/95 mm Hg) * No cardiac arrhythmia requiring anti-arrhythmic medication * Beta blocker or calcium channel blocker allowed * Patients on digitalis that cannot be discontinued not allowed * No Mobitz II second degree block without a pacemaker (first degree or Mobitz I second degree block, bradyarrhythmias, or sick sinus syndrome require Holter monitoring and evaluation by cardiology) * No uncontrolled dysrhythmia * No poorly controlled angina * No other cardiac disease * No history of allergic reaction attributed to compounds of similar chemical or biological composition to FR901228 * No ongoing or active infection * No iatrogenic immune deficiency or immune deficiency secondary to an underlying disorder * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * Potassium ≥ 4.0 mmol/L * Magnesium ≥ 2.0 mg/dL * No other uncontrolled illness * No psychiatric illness or social situation that would preclude study compliance * No concurrent anticancer biologic agents * No more than 1 prior chemotherapy regimen for sarcoma * Adjuvant chemotherapy preceding disease relapse is considered 1 prior chemotherapy regimen * Patients with GIST may have received up to 3 prior chemotherapy regimens comprising imatinib mesylate and/or sunitinib malate provided no other chemotherapy agents were used * No prior FR901228 (depsipeptide) * At least 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin) * No prior cumulative doxorubicin dose \> 500 mg/m\^2 * No other concurrent anticancer chemotherapy * At least 4 weeks since prior radiotherapy * No concurrent anticancer radiotherapy * At least 4 weeks since prior surgery * No prior organ transplantation * Recovered from all prior therapy * No concurrent medications that cause QTc prolongation * No concurrent combination highly active anti-retroviral therapy for HIV-positive patients * No other concurrent drugs known to have histone deacetylase inhibitor activity (e.g., sodium valproate) * No other concurrent investigational agents * No other concurrent anticancer agents