This trial is testing a combination of NBTXR3, radiation therapy, and pembrolizumab to treat patients with head and neck squamous cancer that has come back or spread to other parts of the body. NBTXR3 may make tumors more sensitive to radiation therapy. Radiation therapy, such as stereotactic body radiation therapy, uses special equipment to focus high doses of radiation on tumors with fewer doses over a shorter period, which may kill more tumor cells with less damage to normal tissue. Immunotherapy with monoclonal antibodies, such as pembrolizumab, may help the body's immune system attack