Decitabine in Treating Patients With Metastatic Papillary Thyroid Cancer or Follicular Thyroid Cancer Unresponsive to Iodine I 131

Inclusion Criteria:

* Histologically confirmed papillary thyroid or follicular thyroid carcinoma:

  * Differentiated disease;

    * Metastatic disease documented by ultrasound, computed tomography (CT) scan (without iodinated contrast), or MRI - All metastatic disease foci =\< 10 mm in all dimensions
* Must have been treated with total or near-total thyroidectomy AND at least 1 course of iodine I 131 (131I)(\>=29.9 mCi) OR demonstrated negative uptake on a postoperative low-dose131I scan
* Must have undergone whole body 131I scan 1-3 days after administration of =\< 5.5 mCi of 131I demonstrating no visible iodine uptake within the lesions unless demonstrated negative uptake on a postoperative low-dose131I scan within the past 12 weeks:

  * Must have 24-hour urine iodine excretion =\< 500 mcg within 1 week of 131I scan
* Must be receiving thyroid hormone therapy AND have thyroid-stimulating hormone level =\< 0.5 mU/L
* No known brain metastases
* Performance status:

  * Eastern Cooperative Oncology Group (ECOG) 0-2 OR Karnofsky 60-100%
* Hematopoietic:

  * Absolute neutrophil count \>= 1,500/mm3;
  * Platelet count \>= 100,000/mm3;
  * White Blood Count (WBC) \>= 3,000/mm3
* Hepatic:

  * aspartate aminotransferase-alanine aminotransferase (AST and ALT) =\< 2.5 times upper limit of normal;
  * Bilirubin normal
* Renal:

  * Creatinine not elevated OR
  * Creatinine clearance \>= 60 mL/min
* Cardiovascular:

  * No symptomatic congestive heart failure;
  * No unstable angina pectoris;
  * No cardiac arrhythmia
* Not pregnant or nursing
* Negative pregnancy test
* Fertile patients must use effective contraception
* No prior allergic reaction attributed to compounds of similar chemical or biological composition to decitabine
* No concurrent uncontrolled illness
* No active or ongoing infection
* No psychiatric illness or social situation that would preclude study compliance
* No prior cytotoxic chemotherapy for thyroid cancer
* At least 6 months since prior external beam radiotherapy administered for locoregional disease in the thyroid bed or to the cervical or upper mediastinal lymph node regions (no more than 6,000 cGy)
* More than 6 months since other prior radiotherapy and recovered
* More than 6 months since prior therapeutic 131I \> 10 mCi
* More than 18 months since prior cumulative 131I activity of at least 500 mCi
* More than 12 months since prior amiodarone (Unless 24-hour urinary iodine excretion is =\< 500 mcg)
* No concurrent combination antiretroviral therapy for HIV-positive patients
* No other concurrent anticancer therapy
* No other concurrent investigational agents
* More than 6 months since prior intrathecal iodinated contrast (Unless 24-hour urinary iodine excretion is =\< 500 mcg)
* More than 3 months since prior IV or oral iodinated contrast for radiographic studies (Unless 24-hour urinary iodine excretion is =\< 500 mcg)