This phase II trial studies the effect of selpercatinib given before surgery in treating patients with thyroid cancer whose tumors have RET alterations (changes in the genetic material \[deoxyribonucleic acid (DNA)\]). Selpercatinib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Giving selpercatinib before surgery may help shrink the tumors and help control the disease.

PRIMARY OBJECTIVE: I. To evaluate the efficacy of neoadjuvant selpercatinib in medullary thyroid cancer by objective response rate (ORR) per RECIST (standard Response Evaluation Criteria in Solid Tumors \[RECIST\]). SECONDARY OBJECTIVES: I. To evaluate the efficacy of neoadjuvant selpercatinib in medullary thyroid cancer by ORR per modified neck RECIST. II. To evaluate the efficacy of neoadjuvant selpercatinib in medullary thyroid cancer per surgical margin status, which is categorized as R0, R1, and R2 surgical resection. III. To evaluate the safety profile of neoadjuvant selpercatinib. IV. To evaluate the efficacy of neoadjuvant selpercatinib on progression-free survival (PFS), including overall PFS and locoregional PFS. V. To measure changes in expected and actual surgical morbidity/complexity as well as evaluate changes of R0/R1 resection rates in pre-specified extrathyroidal anatomic target interfaces before and after selpercatinib treatment. EXPLORATORY OBJECTIVES: I. In patients with differentiated thyroid cancer \[DTC\] and anaplastic thyroid cancer \[ATC\] only, to evaluate the efficacy of neoadjuvant selpercatinib by ORR per RECIST (standard RECIST and modified neck RECIST), surgical margin status (R0/R1 versus \[vs.\] R2), safety profile, surgical morbidity/complexity, PFS and overall survival (overall survival \[OS\], ATC only). II. To define and measure changes of patient-reported outcomes and quality of life as measured by MD Anderson Symptom Inventory (MDASI) and European Quality of Life Five Dimension (EQ-5D) in patients with RET-altered thyroid cancer who receive selpercatinib treatment. III. To explore translational endpoints in selpercatinib neoadjuvant therapy with biopsies/tissue collection before selpercatinib treatment and during surgery. IV. To explore peripheral and tissue measures associated with selpercatinib mechanisms of resistance in patients who experience disease progression after selpercatinib treatment. OUTLINE: Patients receive selpercatinb orally (PO) twice daily (BID) on days 1-28. Treatment repeats every 28 days for up to 7 cycles in the absence of disease progression or unacceptable toxicity. Patients then undergo standard of care surgery. After completion of study treatment, patients are followed up for disease progression status every 3-4 months for the first 2 years. ATC patients continue follow-up every 6 months for year 3 and 4, and once in year 5.