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