Romidepsin in Treating Patients With Recurrent and/or Metastatic Thyroid Cancer That Has Not Responded to Radioactive Iodine

Inclusion Criteria: Histologically or cytologically confirmed non-medullary thyroid carcinoma, including the following cell types: Papillary Follicular Variants of papillary or follicular Hürthle cell Recurrent and/or metastatic disease Measurable disease At least 1 unidimensionally measurable lesion >= 20 mm by conventional techniques OR >= 10 mm by spiral CT scan Progressive disease during or after prior treatment, as defined by >= 1 of the following criteria: Presence of new or progressive lesions on CT scan or MRI New lesions on bone or positron-emission tomography scan Rising thyroglobulin level Minimum of 3 consecutive rises with an interval of >= 1 week between each determination Refractory to radioactive iodine (RAI) Absent or insufficient RAI-uptake documented by whole-body RAI scan within the past 6 months At least 1 lesion with absent RAI-uptake required for insufficient uptake No known brain metastases Performance status - Karnofsky 60-100% WBC >= 3,000/mm^3 Absolute neutrophil count >= 1,500/mm^3 Platelet count >= 100,00/mm^3 Bilirubin normal AST and ALT =< 2.5 times upper limit of normal Chronic active viral hepatitis allowed provided patient is clinically stable and fulfills liver function eligibility criteria Creatinine normal Creatinine clearance >= 60 mL/min QTc =< 480 msec by ECG ST segment depression < 2 mm LVEF >= 50 % by echocardiogram No left ventricular hypertrophy, as defined by end-diastolic wall thickness > 12 mm in both the left ventricular posterior wall as well as septum or restrictive cardiomyopathy No history of any of the following cardiac diseases: Canadian Cardiovascular Society (CCS) class II-IV angina pectoris Myocardial infarction within the past 12 months Sustained ventricular tachycardia, ventricular fibrillation, Torsade de Pointes, or cardiac arrest unless currently addressed with an automatic implantable cardioverter defibrillator Any cardiac arrhythmia requiring digitalis or another antiarrhythmic medication other than a beta blocker or calcium channel blocker No uncontrolled hypertension (i.e., blood pressure >= 160/95) Mobitz II second degree block in patients who do not have a pacemaker First degree or Mobitz I second degree block, bradyarrhythmias or sick sinus syndrome require Holter monitoring and evaluation by cardiology Uncontrolled dysrhythmias No history of congenital long QT syndrome Not pregnant or nursing Negative pregnancy test Fertile patients must use effective contraception Thyroid stimulating hormone normal or suppressed No history of allergic reaction attributed to compounds of similar chemical or biologic composition to FR901228 No ongoing or active infection No psychiatric illness or social situation that would preclude study participation No other concurrent uncontrolled illness At least 4 weeks since prior biologic or targeted agents (e.g., interferon alfa, thalidomide, octreotide, or cetuximab) No concurrent antineoplastic biologic agents No prior FR901228 (depsipeptide) No prior cytotoxic chemotherapy Cytotoxic chemotherapy as a radiosensitizer allowed provided >= 3 months since prior administration No other concurrent antineoplastic chemotherapy Not specified At least 4 weeks since prior external beam radiation therapy Documented disease progression required if patient received external beam radiotherapy to index lesions At least 3 months since prior RAI therapy Diagnostic studies using =< 12 mCi of RAI are not considered RAI therapy No concurrent antineoplastic radiotherapy At least 2 weeks since prior anticancer cyclooxygenase-2 (COX-2) inhibitors, isotretinoin, or complementary medications At least 4 weeks since prior tyrosine kinase inhibitors (e.g., gefitinib or erlotinib) No other concurrent investigational agents No other concurrent anticancer therapy No concurrent drugs known to have histone deacetylase inhibitor activity (e.g., valproic acid) No concurrent combination anti-retroviral therapy for HIV-positive patients No concurrent hydrochlorothiazide No concurrent treatment dose warfarin No concurrent agents that cause QTc prolongation Concurrent daily aspirin given after myocardial infarction or COX-2 inhibitors at standard anti-inflammatory or pain doses allowed