Selpercatinib Before Surgery for the Treatment of RET-Altered Thyroid Cancer

Inclusion Criteria: * Patients with RET-altered thyroid cancer who present with locally advanced primary tumor, defined as T3 or T4 by imaging or invasive/bulky nodal disease, or with recurrent/residual invasive/bulky nodal disease will be enrolled in this trial, regardless of whether distant metastases are present or not * At least 12 years of age on the day of signing informed consent * Pathologic findings supporting the clinical impression of medullary thyroid carcinoma, papillary thyroid carcinoma, poorly differentiated thyroid carcinoma, or anaplastic thyroid carcinoma. Diagnosis of anaplastic thyroid carcinoma may include consistent with or suggestive of terminology associated with: anaplastic thyroid carcinoma, undifferentiated carcinoma, squamous carcinoma; carcinoma with spindled, giant cell, or epithelial features; poorly differentiated carcinoma with pleomorphism, extensive necrosis with tumor cells present * Having an activating RET gene alteration (fusion or mutation). The RET alteration result should be generated from a laboratory with Clinical Laboratory Improvement Act (CLIA), ISO/EIC, College of American Pathologists (CAP), or other similar certification that clearly denotes the presence of a RET alteration in tumor, or institutional-approved cell free DNA blood test for RET alteration * Prior multikinase inhibitors (MKIs) with anti-RET activity are allowed. The specific agent(s), duration of treatment, clinical benefit, and reason for discontinuation (e.g., progressive disease \[PD\], drug toxicity, or intolerance) should be documented for all kinase inhibitors the patient has been exposed to * At least one measurable lesion as defined by RECIST 1.1 * Surgical morbidity/complexity score of 1 to 4 (moderate, severe, very severe, or unresectable) * Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2 (age \>= 16 years) or Lansky Performance Score (LPS) \>= 40% (age \< 16 years) with no sudden deterioration 2 weeks prior to study registration * Absolute neutrophil count (ANC) \>= 1500/uL * Hemoglobin \>= 9 g/dL (5.58 mmol/L) * Platelets \>= 100,000/uL * Total bilirubin =\< 1.5 X upper limit of normal (ULN) (Except participants with a documented history of Gilbert syndrome who must have a total bilirubin \< 3 X ULN) * Alanine Aminotransferase (ALT)/Aspartate Aminotransferase (AST) \< 2.5 X ULN OR \< 5 X ULN if the liver has tumor involvement * Normal serum potassium, calcium, and magnesium levels (may be receiving supplements). Grade 1 hypocalcemia (corrected serum calcium \> 8) is acceptable * Willing to undergo tumor biopsy prior to trial treatment, unless in the opinion of the treating physician, a biopsy is not feasible or safe. Subjects must be willing to ultimately undergo surgery if their tumor becomes surgically resectable * Ability to comply with outpatient treatment, laboratory monitoring, and required clinic visits for the duration of study participation * Willing and able to provide written informed consent signed by study patient (or legally acceptable representative if applicable) * Willingness of men with partners of childbearing potential or women of childbearing potential to use a highly effective contraceptive method during treatment with study drug and for 3 months following the last dose of study drug. Male study participants should refrain from sperm donation during study treatment and for up to 6 months following the last dose of selpercatinib Note: * Unless not allowed by local regulations, women of childbearing potential who are abstinent (if this is complete abstinence, as their preferred and usual lifestyle) or in a same-sex relationship (as part of their preferred and usual lifestyle) must agree to either remain abstinent or stay in a same-sex relationship without sexual relations with males. Periodic abstinence (e.g., calendar, ovulation, symptothermal, post ovulation methods), declaration of abstinence just for the duration of the trial, and withdrawal are not acceptable methods of contraception * A postmenopausal woman will be defined as having no menses for 12 months without an alternative medical cause. Male sterility will be defined as only men sterilized surgically. For male patients with a pregnant partner, a condom should be used for contraception. For male patients with a non-pregnant female partner of child-bearing potential and woman of childbearing potential one of the following birth control methods with a failure rate of less than 1% per year when used consistently and correctly are recommended: * Combined estrogen and progesterone containing hormonal contraception associated with inhibition of ovulation given orally, intravaginally, or transdermally * Progesterone-only hormonal contraception associated with inhibition of ovulation given orally, by injection, or by implant * Intrauterine device (IUD) * Intrauterine hormone-releasing system (IUS) * Bilateral tubal occlusion * Vasectomized partner * Sexual abstinence * Women of childbearing potential must have a negative pregnancy test (serum) documented at screening and then negative serum or urine pregnancy testing at day 1 of every treatment cycle (exception: negative pregnancy testing within 21 days prior to cycle 1 day 1 \[C1D1\] is allowed) Exclusion Criteria: * An additional validated oncogenic driver that could cause resistance to selpercatinib treatment (if known) * Prior treatment with a selective RET inhibitor(s) (pralsetinib \[BLU-667\], including investigational selective RET inhibitor\[s\]) * Investigational agent or anticancer therapy (including chemotherapy, biologic therapy, or immunotherapy) within 5 half-lives or 3 weeks (whichever is shorter) prior to planned start of selpercatinib * Exception: Patients with ATC * No concurrent investigational anti-cancer therapy is permitted * Major surgery (excluding placement of vascular access and diagnostic procedures) within 4 weeks prior to planned start of selpercatinib * Exception: Patients with ATC * Radiotherapy with a limited field of radiation for palliation within 1 week of the first dose of study treatment, with the exception of patients receiving radiation to more than 30% of the bone marrow or with a wide field of radiation, which must be completed at least 4 weeks prior to the first dose of study treatment * Any unresolved toxicities from prior therapy greater than Common Terminology Criteria for Adverse Events (CTCAE) grade 1 at the time of starting study treatment with the exception of alopecia and grade 2, prior platinum therapy related neuropathy * Symptomatic primary central nervous system (CNS) tumor, metastases, leptomeningeal carcinomatosis, or untreated spinal cord compression * Exception: Patients are eligible if neurological symptoms and CNS imaging are stable and steroid dose is stable for 14 days prior to the first dose of selpercatinib and no CNS surgery or radiation has been performed for 28 days, 14 days if stereotactic radiosurgery (SRS) * Patients with clinically significant active cardiovascular disease, Torsades de pointes, or history of myocardial infarction within 6 months prior to planned start of study treatment or prolongation of the QT interval corrected for heart rate using Fridericia's formula (QTcF) \> 470 msec * Patients with clinically significant active malabsorption syndrome or other condition likely to affect gastrointestinal absorption of the drug * Use of a concomitant medication that is known to cause QTc prolongation * Active uncontrolled systemic bacterial, viral, or fungal infection, or serious ongoing intercurrent illness, such as uncontrolled hypertension (systolic blood pressure \[BP\] \>= 140 mmHg or diastolic BP \>= 90 mmHg per CTCAE) or diabetes, despite optimal treatment. Screening for chronic conditions is not required * Uncontrolled symptomatic hyperthyroidism or hypothyroidism * Exception: Patients with papillary thyroid cancer (PTC) * Uncontrolled symptomatic hypercalcemia or hypocalcemia * Pregnancy or lactation * Active second malignancy other than minor treatment of indolent cancers * Exception: Patients with PTC or patients with stable pheochromocytoma in MEN2 * History of severe hypersensitivity (\>= grade 3) to selpercatinib and/or any of its excipients