Patient description: A 46-year-old woman presents with a 9 month history of weight loss (20 lb), sweating, insomnia and diarrhea. She reports to have been eating more than normal and that her heart sometimes races for no reason. On physical examination her hands are warm and sweaty, her pulse is irregular at 110bpm and there is hyperreflexia and mild exophthalmia.

Clinical trial eligibility criteria: eligible ages (years): 18.0-999.0,  Poorly Differentiated Thyroid Gland Carcinoma Recurrent Thyroid Gland Carcinoma Stage IVA Thyroid Gland Follicular Carcinoma Stage IVA Thyroid Gland Papillary Carcinoma Stage IVB Thyroid Gland Follicular Carcinoma Stage IVB Thyroid Gland Papillary Carcinoma Stage IVC Thyroid Gland Follicular Carcinoma Stage IVC Thyroid Gland Papillary Carcinoma Histological or cytological confirmation of thyroid carcinoma of follicular origin (including papillary, follicular, or poorly differentiated subtypes and their respective variants); note: medullary and anaplastic thyroid cancers are excluded; Hurthle cell carcinomas are excluded (defined as having an invasive tumor composed of > 75% oncocytic [Hurthle] cells lacking the nuclear features of papillary carcinoma, tumor necrosis, and marked mitotic activity); patients with oncocytic (Hurthle cell) variants of papillary thyroid carcinoma (defined as a tumor composed of a majority of oncocytic [Hurthle] cells having the nuclear features of papillary carcinoma) are eligible to participate RAI-avid lesion on a radioiodine scan (a diagnostic, post-therapy, or post-ablation scans) performed =< 12 months prior to registration, which suggests that therapy with 131I is justifiable in the judgment of the investigator Measurable disease; (NOTE: a malignant lymph node is considered measurable if 1) it is noted to be RAI-avid on radioactive iodine imaging [diagnostic or post-therapy whole body scans acceptable] and it measures >= 1 cm in the long axis, 2) it is pathologically proven to be involved with thyroid cancer [by cytology or pathology] and it measures >= 1 cm in the long axis, or 3) its short axis is >= 1.5 cm when assessed by computed tomography [CT] scan) Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2 Able to swallow and retain orally-administered medication with no clinically significant gastrointestinal abnormalities that may alter absorption Absolute neutrophil count (ANC) >= 1500/mm^3 Platelet count >= 100,000/mm^3 Hemoglobin > 9.0 g/dL Total bilirubin =< 1.5 x upper limit of normal (ULN) Aspartate transaminase (AST) =< 2.5 x ULN (or =< 5x ULN in presence of liver metastases)  therapy =< 6 months prior to registration; note: A diagnostic study using < 10 mCi of 131I is not considered 131I therapy External beam radiation therapy =< 28 days prior to registration; note: previous treatment with radiation is allowed if the investigator judges it will not compromise patient safety on the study Having been treated with a total cumulative (lifetime) 131I therapeutic activity > 800 mCi (excluding 131I activity administered for diagnostic scans) Treatment with chemotherapy or targeted therapy (e.g. tyrosine kinase inhibitor) =< 28 days prior to registration Prior exposure to mitogen-activated protein kinase kinase (MEK), RAS, or RAF inhibitors (note: previous exposure to sorafenib is allowed) OR history of hypersensitivity to selumetinib, thyrotropin alpha (Thyrogen), or any excipient agents Unresolved toxicity > Common Terminology for Adverse Events (CTCAE) grade 2 from previous anti-cancer therapy, except for alopecia Cardiac conditions as follows Uncontrolled hypertension (blood pressure [BP] >=150/95 mmHg despite medical therapy) Left ventricular ejection fraction < 55% measured by echocardiography Atrial fibrillation with a ventricular rate > 100 beats per minute (bpm) on electrocardiogram (ECG) at rest