NBTXR3, Radiation Therapy, and Pembrolizumab for the Treatment of Recurrent or Metastatic Head and Neck Squamous Cell Cancer

Inclusion Criteria: * Patients with biopsy proven R/M HNSCC that is considered incurable by local therapies. * Participant must have at least 2 lesions * At least one lesion will be the target lesion, which will be injected with NBTXR3 and radiated and must be in either the head and neck (HN) or lung or liver. * The other lesion will be a non-target lesion, which will not be treated with NBTXR3 or RT, but will be followed for response. * Prior systemic therapy (i.e., chemotherapy or targeted therapy) given as part of multimodal treatment for locally advanced disease is allowed. * Prior anti-PD-1/L1 therapy allowed in the PD-1 refractory cohort (cohort 2) * Have results from testing of human papillomavirus (HPV) status for oropharyngeal cancer defined as p16 immunohistochemistry (IHC) testing using CINtec p16 Histology assay, or equivalent, and a 70% cutoff point. * If HPV status previously tested using aforementioned method or an equivalent, no additional testing needed. * Oral cavity, hypopharynx, and larynx cancer are not required to undergo HPV testing by p16 IHC as by convention these tumor locations are assumed to be HPV negative * Have provided tissue for PD-L1 biomarker analysis from a core or excisional biopsy, fine needle aspirate (FNA) not adequate. * A newly obtained biopsy (within 90 days prior to NBTXR3 injection is preferred), but an archival sample is acceptable. * PD-1/L1 naive patients with 1% =\< combined positive score (CPS) \< 20 based on IHC testing. * PD-1/L1 refractory patients all CPS levels allowed * Amenable to undergo the image guided intratumoral/intranodal injection of NBTXR3 in up to 3 target lesions, as per investigator or treating physician discretion. * For the HN target lesions (\< 60 cm\^3 per site, total volume \< 120 cm\^3) may be injected and irradiated, including the primary tumor and involved lymph node(s). * For the lung or liver target lesion no maximum volume threshold has been defined. However, target lesions must be amenable to receive NBTXR3 injection and RT (50 Gy in 4 fx or 60 Gy in 10 fx) * The selected target lesion and non-target lesion 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 * Target lesion(s) must be located in the HN or lung or liver * Target lesion must be amenable to receive RT regimens specified in this protocol at the discretion of the investigator or treating radiation oncologist. * Nodal target lesions must be ≥15mm (short axis) based on CT (slice thickness of 5 mm or less) or 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 * Calculated (Calc.) creatinine clearance \> 40 mL/min * Total bilirubin =\< 2.0 mg/dL * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.5 x upper limit of normal (ULN) or =\< 5 x ULN for patients with liver metastasis * For patients with lung metastases, adequate lung function with expiratory volume in 1 second (FEV1) \>= 0.8 L or \>= 35% predicted and carbon monoxide diffusing capability (DLCO) \>= 40% with or without bronchodilator within 28 days prior to NBTXR3 injection * Patients who meet the criterion above without oxygen (O2), but need acute (started within 7 +/- 3 days) supplemental oxygen due to tumor-caused obstruction/hypoxia are eligible, provided the amount of the O2 needed has been stable * 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 anti-PD-1 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: * Diagnosis other than HNSCC R/M with disease that is suitable for local therapy administered with curative intent * Less than 6-month time interval from prior radiation to the HN given as part of multimodal treatment for locally advanced disease * Prior radiation to the lung or liver target lesions * 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 or immunotherapy within 4 weeks prior to NBTXR3 injection. * Except anti-PD-1 therapy for patients assigned to cohort 2 (PD-1/L1 refractory), which will not require a washout window. * A reduced washout window may be considered for therapies with short half-lives (i.e., kinase inhibitors) after discussion with Nanobiotix and investigator * 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 * Symptomatic central nervous system metastases and/or carcinomatous meningitis * Participants with previously treated brain metastases may participate provided that those lesions are radiologically stable (i.e., without evidence of progression for at least 4 weeks by repeat imaging at screening), clinically stable, and without requirement of steroid treatment for at least 14 days prior to NBTXR3 injection * 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 * At screening, past medical history of: * Drug related pneumonitis * Idiopathic pulmonary fibrosis (IPF) * Unresolved organizing pneumonia (i.e., bronchiolitis obliterans, cryptogenic organizing pneumonia) * Unresolved radiation related * Pneumonitis * Bronchopulmonary hemorrhage * Abdominal hemorrhage * Any grade 4 radiation related toxicity * Unresolved gastrointestinal (GI) related events * Diverticulitis * Intra-abdominal abscess * GI obstructions * Abdominal carcinomatosis * Any known risk factor for bowel perforation * Any live-virus vaccine therapy used for prevention of infectious diseases administered within 4 weeks prior to NBTXR3 injection * 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 * A history of prior malignancy other than the HNSCC. * Subjects with a history of basal or squamous cell carcinoma of the skin, superficial bladder cancer, in situ cervical or breast cancer, prostate cancer in watchful wait, or those that have received curative therapy with no disease recurrence for \>= 2 years may be enrolled * 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 anti-PD-1. * 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