Iodine I-131 With or Without Selumetinib in Treating Patients With Recurrent or Metastatic Thyroid Cancer

This phase II trial studies how well iodine I-131 works with or without selumetinib in treating patients with thyroid cancer that has returned (recurrent) or has spread from where it started to other places in the body (metastatic). Many thyroid cancers absorb iodine. Due to this, doctors often give radioactive iodine (iodine I-131) alone to treat thyroid cancer as part of standard practice. It is thought that the more thyroid tumors are able to absorb radioactive iodine, the more likely it is that the radioactive iodine will cause those tumors to shrink. Selumetinib may help radioactive iodine work better in patients whose tumors still absorb radioactive iodine. It is not yet known whether iodine I-131 is more effective with or without selumetinib in treating thyroid cancer.