Suberoylanilide Hydroxamic Acid in Treating Patients With Metastatic and/or Locally Advanced or Locally Recurrent Thyroid Cancer

Inclusion Criteria: * Histologically confirmed thyroid cancer * One of the following subtypes: * Papillary thyroid cancer * Follicular thyroid cancer * Hürthle cell thyroid cancer * Insular thyroid cancer * Medullary thyroid cancer * Mixed histology thyroid cancer * Poorly differentiated thyroid cancer * Tall-cell thyroid cancer * Metastatic and/or locally advanced or locally recurrent disease * Measurable disease, defined as ≥ 1 unidimensionally measurable lesion ≥ 20 mm by conventional techniques OR ≥ 10 mm by spiral CT scan * Lesions in a previously irradiated area allowed provided there has been subsequent disease progression of the irradiated lesions * The following are not considered measurable disease: * Bone lesions * Leptomeningeal disease * Ascites * Pleural or pericardial effusion * Lymphangitis cutis/pulmonis * Abdominal masses not confirmed and followed by imaging techniques * Cystic lesions * Not a candidate for radioactive iodine I\^131 therapy * Performance status - ECOG 0-1 * At least 6 months * WBC ≥ 3,000/mm\^3 * Absolute neutrophil count ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 * Bilirubin ≤ 1.5 mg/dL * AST and ALT ≤ 2.5 times upper limit of normal * Creatinine ≤ 1.5 mg/dL * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No history of allergic reaction attributed to compounds of similar chemical or biologic composition to study drug * No ongoing or active infection * No psychiatric illness or social situation that would preclude study compliance * No other uncontrolled illness * No other active malignancy except nonmetastatic nonmelanoma skin cancer or carcinoma in situ of the cervix * More than 4 weeks since prior systemic cytotoxic chemotherapy (6 weeks for nitrosoureas or mitomycin) * No more than 2 prior chemotherapy regimens for the treatment of thyroid cancer * See Disease Characteristics * More than 4 weeks since prior external beam radiotherapy * At least 24 weeks since prior radioactive iodine I\^131 therapy * Recovered from prior therapy * More than 4 weeks since prior valproic acid or any other histone deacetylase inhibitor * More than 4 weeks since prior investigational tumor-specific therapy * Concurrent oral or IV bisphosphonates for bony metastases allowed at the discretion of the investigator * No concurrent combination antiretroviral therapy for HIV-positive patients * No other concurrent tumor-specific or investigational therapy * No other concurrent anticancer therapy * No concurrent adjuvant therapy for another cancer