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 (ALT) ≤3 x upper limit of normal * Alkaline phosphatase ≤2.5 x upper limit of normal * Serum creatinine ≤1.5 x upper limit of normal or estimated creatinine clearance \>30 mL/min according to Cockcroft-Gault formula * Hemoglobin \>9 g/dL * Absolute neutrophil count ≥1.5 x10\^9/L * Platelet count ≥75 x10\^9/L * Able to provide informed consent * Acceptable candidate for curative intent radiotherapy and Cemiplimab immunotherapy, in opinion of radiation and medical oncologist, respectively * Life expectancy \>18 months Exclusion Criteria: * Primary tumor originating on the mucosal (non-hair bearing) lip or nose, anogenital (penis, scrotum, vulva, perianal) area * Iatrogenic immunosuppression (\>prednisone 10 mg/day or equivalent within 14 days of initiation of treatment) * Women of child bearing potential unwilling or unable to use effective contraception while receiving treatment with cemiplimab and for 4 months thereafter * Distant metastases * Clinically significant autoimmune disease that requires iatrogenic immunosuppression o For example, severe rheumatoid arthritis requiring disease modifying antirheumatic drugs, such as methotrexate * Current or previous hematopoietic malignancy (leukemia, lymphoma) * Prior allogeneic transplant of solid organ or bone marrow * Concurrent malignancies with \>10% risk of metastasis or death within 2 years * Prior aPD1 immunotherapy or PI3Kδ inhibitor use * Prior radiotherapy for the cutaneous squamous cell carcinoma requiring treatment * Other ongoing cancer therapy o Adjuvant endocrine therapy is permitted for patients with prostate or breast cancer * Uncontrolled HIV or infectious hepatitis (viral load detectable in patient with known infection) * Pregnancy or breastfeeding * Comorbid or diagnostic abnormalities within the last year that would interfere with interpretation of study results