A Study of Radiation Therapy and Cemiplimab for People With Skin Cancer

Inclusion Criteria: * Biopsy proven cutaneous squamous cell carcinoma which is locally advanced * Mixed histology tumors that are predominantly squamous cell carcinoma are eligible * Locally advanced primary tumor is T3-T4 and/or N+ by AJCC and/or UICC 8th edition clinical criteria * T3-T4 primary tumor characteristics noted below: * Non-eyelid tumor \>4 cm in maximum dimension or with bone erosion or invasion, perineural invasion of nerve 0.1 mm or larger, or invasion beyond subcutaneous fat or \>6 mm from granular layer of adjacent normal epidermis * Eyelid tumor \>2 cm or invading adjacent ocular, orbital or facial structures * ≥18 years old * Unresectable or medically inoperable according to local multidisciplinary consensus for reasons such as: * Tumor or regional lymph node metastases that has recurred despite ≥2 prior surgical procedures, with another curative resection unlikely * Tumor or nodal disease with significant local invasion that precludes complete resection * Tumor or nodal disease in anatomically challenging area where surgery may result in significant disfigurement or dysfunction (amputation of nose, ear, eye, digit, limb, etc) * Medical contraindication to surgery * Patient refusal of surgery due to anticipate morbidity * ECOG ≤2 * Adequate bone marrow and metabolic function (by blood tests) * Total bilirubin ≤1.5 x upper limit of normal * Aspirate aminotransferase (AST) ≤3 x upper limit of normal * Alanine aminotransferase (A…