Dabrafenib, Trametinib, and IMRT in Treating Patients With BRAF Mutated Anaplastic Thyroid Cancer

Inclusion Criteria: * Pathologic (histologic or cytologic) diagnosis of anaplastic thyroid cancer (a diagnosis that is noted to be ?consistent with anaplastic thyroid cancer? with the presence of a thyroid mass is acceptable; pathology showing additional types of thyroid cancer is allowed) * Note: Tissue collection for central review is mandatory, but central review is not required for eligibility. Due to the aggressiveness of this disease, treatment will be started prior to central review. * Presence of BRAF mutation (V600E or V600K) in tumor tissue. * Eastern Cooperative Oncology Group (ECOG) performance status \< 2. * Absolute neutrophil count \> 1,000/mcL. * Hemoglobin \>= 9.0 g/dl (Note: The use of transfusion or other intervention to achieve hemoglobin \[Hgb\] \>= 9.0 g/dl is acceptable). * Platelets \> 75,000/mcL. * Total bilirubin \< 1.5 x institutional upper limit of normal (unless due to Gilbert?s disease). * Aspartate aminotransferase (AST)(serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) \< 2.5 x institutional upper limit of normal. * Serum creatinine \< 1.5 x institutional upper limit of normal. * Female patients of childbearing potential are required to have a negative serum pregnancy test within 14 days prior to the first dose of study medication. * Females are required to use an effective method of contraception from the time of negative serum pregnancy test, throughout the st…