Losartan, Pembrolizumab and Stereotactic Body Radiation Therapy for the Treatment of Patients With Locally Recurrent, Refractory or Oligometastatic Head and Neck Squamous Cell Carcinoma

Inclusion Criteria: * Histologically or cytologically confirmed locoregionally recurrent, refractory, or oligometastatic (at most 4 lesions) squamous cell carcinoma of the head and neck not amenable to curative resection * p16 status known for base of tongue, soft palate, and tonsil cancers * Tumor amenable to sequential biopsies, and patients willing to undergo sequential tumor biopsies so long as the treating investigator considers them to be clinically safe * Prior radiotherapy to the head and neck is allowed. Disease should be limited to up to 4 sites of active disease in the head and neck and/or distant metastatic sites if deemed safely treatable by physician, or adjacent sites treatable in single contiguous target volume with a recommended maximum total tumor dimension (GTV) of \< 7.5 cm. However, larger volumes may be allowed after discussion with primary investigator (PI) and careful review of radiation dose constraints * Prior systemic therapy is allowed. Patients with locoregional relapses where radiation alone would be indicated are allowed to enroll without prior systemic therapy * Presence of measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST 1.1) with a target on a computed tomography (CT) scan or magnetic resonance imaging (MRI) available for review * Combined positive score (CPS) \> 1% * Age ≥ 18 years at time of consent * Eastern Cooperative Oncology Group (ECOG) performance status 0 - 1 * Leukocytes ≥ 3 × 10\^9/L * Absolute neutrophil count ≥ 1.5 × 10\^9/L * Platelets ≥ 100 × 10\^9/L * Hemoglobin (Hgb) ≥ 9 g/dL, transfusions may be used to raise Hgb to ≥ 9 g/dL (no washout required) * Total bilirubin ≤ 1.5 × institutional upper limit of normal (ULN) * Aspartate transaminase (AST) / alanine transaminase (ALT) ≤ 2.5 × institutional ULN * Creatinine within normal institutional limits OR creatinine clearance ≥ 30 mL/min/1.73 m\^2 for patients with creatinine above institutional ULN * The effects of losartan on the developing human fetus are unknown. For this reason, individuals of childbearing potential and male participants with partners of childbearing potential, must agree to use methods of contraception for the duration of study participation (including dosing interruptions) and for up to 3 months after last study treatment; or be surgically sterilized * Ability to understand and willingness to sign and date the informed consent form * Stated ability and willingness to adhere to the study visit schedule and protocol requirements Exclusion Criteria: * Nasopharyngeal carcinoma, salivary gland carcinoma or primary skin squamous cell carcinoma (SCC) * Prior treatment with an anti-PD-1, anti-PD-L1, or anti-PD-L2 antibody * Chemotherapy or other anti-cancer therapy within 3 weeks prior to study day 1 * Hypersensitivity to losartan or any component of the formulation * Radiation therapy within 6 months prior to study day 1 * Patients with disease surrounding \> 50% of the carotid * Participant who has not recovered to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) grade ≤ 1 from an adverse event (AE) due to previous cancer therapeutics (i.e., chemotherapy, radiation therapy, biologic therapy, and/or experimental therapy) with the exception of alopecia * Major surgery as assessed by the investigator (with the exception of diagnostic biopsy) within ≤ 28 days prior to study day 1 (patients must have completely recovered from any previous surgery prior to study day 1) * Clinically significant bleeding ≤ 4 weeks prior to study day 1 * Requirement for parenteral antibiotics, or any active infection requiring parenteral antibiotic therapy within 4 weeks prior to study day 1 * Clinically significant or uncontrolled diabetes mellitus (hemoglobin A1C ≤ 8.5%). Patients with diabetes mellitus treated with aliskiren ≤ 7 days prior to study day 1 are excluded * Active autoimmune disorders that have required systemic treatment with disease modifying agents, corticosteroids, or immunosuppressive drugs in the past 2 years are excluded. Patients with autoimmune disorder or well-managed or inactive autoimmune disorders, such as Hashimoto's thyroiditis, may be allowed at the discretion of the PI * Current use of systemic corticosteroids equivalent to \>10 mg of prednisone per day * Current use of angiotensin receptor blockers (ARBs) or angiotensin converting enzyme (ACE) inhibitors for management of hypertension * Clinically significant cardiovascular, pulmonary, endocrine, neurologic, gastrointestinal or genitourinary disease unrelated to underlying solid tumor that in the judgment of the investigator should preclude treatment with losartan * Any other active malignancy except for low-risk prostate cancer previously treated or under active surveillance, uncomplicated and cured basal cell carcinoma, or squamous cell carcinoma of the skin within 5 years of study entry * Known history of positive hepatitis C (HCV) antibody, hepatitis B (HBV) surface antigen (HbsAg and HBV core Ab positive), or human immunodeficiency virus (HIV) antibody results. Patients with positive antibody tests are eligible with negative viral loads * Administration of live, attenuated vaccine ≤ 28 days prior to study day 1. Administration of inactivated flu vaccines is allowed * Any prior treatment with losartan or other specific TGF-β-directed therapy * Treatment with another investigational drug or device, or approved therapy for investigational use ≤ 28 days prior to study day 1, or if the half-life of the previous product is known, within 5 times the half-life prior to study day 1, whichever may be longer * Pregnant or breast feeding * Any condition that in the opinion of the investigator would interfere with the participant's safety, compliance while on trial, or understanding or rendering of informed consent