Iodine I 131 and Pazopanib Hydrochloride in Treating Patients With Recurrent and/or Metastatic Thyroid Cancer Previously Treated With Iodine I 131 That Cannot Be Removed By Surgery

Inclusion Criteria: * Subjects must provide written informed consent prior to performance of study-specific procedures or assessments, and must be willing to comply with treatment and follow up; procedures conducted as part of the subject's routine clinical management (e.g., blood count, imaging study) and obtained prior to signing of informed consent may be utilized for screening or baseline purposes provided these procedures are conducted as specified in the protocol * Histologically confirmed diagnosis of well-differentiated thyroid carcinoma (WDTC), including papillary and follicular subtypes, and documented recurrent and/or metastatic disease; patients must have unresectable disease: patients must not be amenable to surgery but prior thyroidectomy is allowed * Patient must have demonstrated evidence of disease progression by RECIST criteria using site assessment of computed tomography (CT)/magnetic resonance imaging (MRI) scans within 12 months (+1 month to allow for variances in patient scanning intervals) prior to study entry or by \> 50% increase in suppressed thyroglobulin levels during this time period * Patients with WDTC must be relatively 131I refractory/resistant as defined by at least one of the following: * One or more measurable lesions with low or absent 131I uptake on the most recent pre-study radioiodine scans, based on a visual review of scans or RAI scan reports * One or more measurable lesions with disease progression by RECIST within 12 months (+…