Re-irradiation With NBTXR3 in Combination With Pembrolizumab for the Treatment of Inoperable Locoregional Recurrent Head and Neck Squamous Cell Cancer

Inclusion Criteria: * Patients with biopsy proven locoregional recurrent squamous cell carcinoma of the head and neck, or second primary HNSCC * Previous documented receipt of at least 30 Gy and up to 70 Gy of radiation for HNSCC with overlapping fields based on actual dose, prescription percentage * 30 Gy for conventional fractionation * 15 Gy for hypofractionation * 10 Gy for single fraction * Time interval from prior radiotherapy to NBTXR3 injection (day 1) of at least 6 months * Not eligible (unresectable) or poor candidate or patient refusal of surgery for HNSCC recurrence * Amenable to undergo the image guided intratumoral/intranodal injection of NBTXR3 by Interventional Radiologist or ear, nose, and throat (ENT) surgeon, as per investigator or treating physician * The target lesion(s) in the head and neck should be measurable as per Response Evaluation Criteria in Solid Tumors (RECIST) version (v)1.1 on cross sectional imaging and repeated measurements at the same anatomical location should be achievable * Up to 3 target lesions may be injected with NBTXR3 and radiated, including the primary tumor and involved lymph node(s) * SBRT cohort: =\< 60 cm\^3 per site, total volume =\< 120 cm\^3 * IMRT/IMPT cohort: =\< 120 cm\^3 per site, total volume =\< 200 cm\^3 * Nodal target lesions must be \>= 15mm (short axis) based on computed tomography (CT) (slice thickness of 5 mm or less) or magnetic resonance imaging (MRI) * Age \>= 18 years * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Hemoglobin \>= 9.0 g/dL * Absolute neutrophil count (ANC) \>= 1,000/mm\^3 * Platelet count \>= 100,000/mm\^3 * Leukocytes \>= 1500/mm\^3 * Creatinine =\< 1.5 x upper limit of normal (ULN) * Calculated (Calc.) creatinine clearance \> 30 mL/min * Total bilirubin =\< 1.5 mg/dL * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.5 x upper limit of normal (ULN) * Serum albumin \> 3.5 g/L * Negative urine or serum pregnancy test =\< 7 days prior to NBTXR3 injection in all women of child-bearing potential (WOCBP). WOCBP must agree to follow instructions for method(s) of contraception for the duration the entire study period and 6 months after the last dose of pembrolizumab treatment. Local laws and regulations may require use of alternative and/or additional contraception methods. WOCBP who are continuously not heterosexually active are exempt from contraceptive requirements but should still undergo pregnancy testing * Signed informed consent form (ICF) indicating that participant understands the purpose of, and procedures required for, the study and is willing to participate in the study Exclusion Criteria: * Locoregional relapse with skin ulceration * Head and neck carcinoma with radiographic evidence of metastasis at screening * Surgery to the head and neck * Excluding diagnostic biopsy * History of severe immune-related adverse events observed with previous immunotherapy (anti-PD-1/L1) or known sensitivity (grade \>= 3) to any excipients * Has received any approved or investigational anti-neoplastic agent within 4 weeks prior to NBTXR3 injection * Except anti-PD-1 therapy, which will not require a washout window * Note: a reduced washout window may be considered for therapies with short half-lives (i.e., kinase inhibitors) after discussion with Nanobiotix and investigator * Active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease-modifying agents, corticosteroids, or immunosuppressive drugs) * Replacement therapy (i.e., thyroxine, insulin, or physiologic corticosteroid replacement \[=\< 10 mg prednisone\] therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment * Has not recovered from adverse events (AEs) due to previous anti-neoplastic or immune-oncology therapy and/or interventions (including radiation) to =\< grade 1 * Participants with alopecia and =\< grade 2 neuropathy may be eligible * Any live-virus vaccine therapy used for prevention of infectious diseases administered within 4 weeks prior to NBTXR3 injection * Except killed-virus Influenza vaccine * Exception of other vaccines (e.g. pneumonia) is at the discretion of the treating physician after conducting a personalized risk assessment on a case by case basis * Prior allogenic stem cell transplantation or organ allograft * Known contraindication to iodine-based or gadolinium-based IV contrast * Active malignancy, in addition to head and neck carcinoma, with the exception of basal cell carcinoma of the skin definitively treated and relapse free within at least 1 year since diagnosis or low risk prostate cancer * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, renal failure, cardiac arrhythmia, or psychiatric illness that would limit compliance with treatment * Known active, uncontrolled (high viral load) human immunodeficiency virus (HIV) or hepatitis B or hepatitis C infection * Female patients who are pregnant or breastfeeding * Women of child-bearing potential and their male partners who are unwilling or unable to use an acceptable method of birth control to avoid pregnancy for the entire study period and up to 6 months, for females, and 220 days for males after the last dose of pembrolizumab * Acceptable methods of contraception are those that, alone or in combination, result in a failure rate of \< 1% per year when used consistently and correctly * Any condition for which, in the opinion of the investigator, participation would not be in the best interest of the participant (e.g., compromise the well-being) or that could prevent, limit, or confound the protocol-specified assessments