Everolimus in Treating Patients With Progressive or Recurrent, Unresectable, or Metastatic Thyroid Cancer

DISEASE CHARACTERISTICS: * Diagnosis of thyroid cancer meeting ≥ 1 of the following criteria: * Progressive or recurrent disease * Metastatic disease * Unresectable disease * Meeting any of the following thyroid cancer subtypes: * Differentiated thyroid cancer (i.e., papillary, follicular, or Hurthle cell disease) that is radio-iodine refractory * Undifferentiated thyroid cancer (i.e., anaplastic disease) * Medullary thyroid cancer * Must have received prior everolimus or other mTOR inhibitor therapy * Patients with history of brain metastasis who are neurologically stable following definitive radiation and/or surgery and do not require corticosteroids allowed PATIENT CHARACTERISTICS: * Karnofsky performance score 70-100% * ANC ≥ 1,500/mm\^³ * Platelet count ≥ 100,000/mm³ * Hemoglobin ≥ 5.6 mmol/L * Serum bilirubin ≤ 1.5 times upper limit of normal (ULN) * ALT and AST ≤ 2.5 times ULN (≤ 5 times ULN for known liver metastases) * Serum creatinine ≤ 2 times ULN * Negative pregnancy test * No other malignancy, except nonmelanoma skin cancer, carcinoma in situ of the cervix, or a malignancy diagnosed and with no current evidence of malignancy within the past 2 years PRIOR CONCURRENT THERAPY: * See Disease Characteristics