Pembrolizumab, Chemotherapy, and Radiation Therapy With or Without Surgery in Treating Patients With Anaplastic Thyroid Cancer

Inclusion Criteria:

* Histological confirmation of, or cytology reported and confirmed, anaplastic thyroid cancer

  * NOTE: A diagnosis reported as ?poorly differentiated carcinoma consistent with anaplastic thyroid cancer? will be accepted
* Absence of prior neck radiotherapy
* Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0 or 1
* Hemoglobin \>= 9.0 g/dL
* White blood cells (WBC)/leukocytes \>= 3500/mm\^3
* Absolute neutrophil count (ANC) \>= 1500/mm\^3
* Platelet count \>= 100,000/mm\^3
* Total bilirubin =\< 1.5 x upper limit of normal (ULN) (except for patients with well-documented Gilbert?s syndrome)
* Aspartate transaminase (AST) =\< 3 x ULN
* Creatinine =\< 1.5 x ULN OR calculated creatinine clearance \>= 50 ml/min using the Cockcroft-Gault formula
* Prothrombin time (PT)/activated partial thromboplastin time (PTT) =\< 1.5 x ULN, unless subject is receiving anticoagulant therapy and PT or activated (a)PTT is within therapeutic range of intended use of anticoagulants
* Negative pregnancy test done =\< 7 days prior to registration, for persons of childbearing potential only

  * NOTE: If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required
  * NOTE: Merck requires an additional pregnancy test if eligibility pregnancy test is \> 72 hours prior to first dose
* Persons of childbearing potential must be willing to use an adequate method of birth control for the course of the study through 120 days after the last dose of study medication

  * NOTE: Abstinence is acceptable if this is the usual lifestyle and preferred method of contraception for the patient
* Persons able to father a child must agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy

  * NOTE: Abstinence is acceptable if this is the usual lifestyle and preferred method of contraception for the patient
* Provide written informed consent
* Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study)
* Willing to provide tissue and blood samples for correlative research purposes

Exclusion Criteria:

* History of non-infectious pneumonitis that required steroids or current pneumonitis
* Any of the following:

  * Pregnant persons
  * Nursing persons
  * Persons of childbearing potential who are unwilling to employ adequate contraception
* Any autoimmune disease such as inflammatory bowel disease, including but not limited to:

  * Ulcerative colitis
  * Crohn's disease
  * Rheumatoid arthritis
  * Systemic sclerosis
  * Systemic lupus erythematosus
  * Autoimmune hepatitis
  * Other autoimmune disease not listed above
  * NOTE: Subjects with autoimmune thyroid disease and diabetes mellitus type I will be allowed
* Uncontrolled intercurrent illness including, but not limited to,

  * Ongoing or active infection
  * Symptomatic congestive heart failure
  * Unstable angina pectoris
  * Cardiac arrhythmia, or
  * Psychiatric illness/social situations that would limit compliance with study requirements
* Other active malignancy =\< 6 months prior to registration

  * EXCEPTIONS: Non-melanotic skin cancer or carcinoma-in-situ of the cervix or prostate cancer confined to prostate gland with Gleason score \< 6 or prostate-specific antigen (PSA) \< 1
  * NOTE: If there is a history of prior malignancy, they must not be receiving other treatment for their cancer; ongoing adjuvant hormonal treatment for breast cancer is allowed
* Prior known allergic reaction to pembrolizumab or its excipients
* Untreated brain metastasis
* Immunocompromised patients and patients known to be human immunodeficiency virus (HIV) positive and currently receiving antiretroviral therapy
* Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm
* Received any live vaccine =\< 30 days prior to registration
* Any of the following conditions =\< 6 weeks prior to registration:

  * Cerebrovascular accident (CVA)
  * Admission for unstable angina
  * Cardiac angioplasty or stenting or coronary artery bypass graft surgery
  * Pulmonary embolism or untreated deep venous thrombosis (DVT)
  * Arterial thrombosis
  * Class III or IV heart failure as defined by the New York Heart Association (NYHA) functional classification system