Cemiplimab in Treating Patients With Recurrent and Resectable Stage II-IV Head and Neck Cutaneous Squamous Cell Cancer Before Surgery

Inclusion Criteria: * Biopsy-proven, primary or recurrent stage II-IV cutaneous squamous cell carcinoma of the head and neck. * Surgical resection must be planned as primary therapy with or without adjuvant radiation therapy. Patients are eligible with previous surgical intervention if they have residual or recurrent disease, and it is greater than 4 weeks since surgery and they have fully recovered from surgery. * Signed informed consent form (ICF).\* * Ability and willingness to comply with the requirements of the study protocol.\* * Age \>= 18 years. * Absolute neutrophil count (ANC) \>= 1500 cells/uL (obtained within 4 weeks \[+/-3 days\] prior to study entry). * White blood cell (WBC) counts \>= 2500/uL (obtained within 4 weeks \[+/-3 days\] prior to study entry). * Lymphocyte count \>= 300/uL (obtained within 4 weeks \[+/-3 days\] prior to study entry). * Platelet count \>= 100,000uL for patients with hematologic malignancies, platelet count \>= 75,000/uL (obtained within 4 weeks \[+/-3 days\] prior to study entry). * Hemoglobin \>= 9.0 g/dL (obtained within 4 weeks \[+/-3 days\] prior to study entry). * Total bilirubin =\< 1.5 x upper limit of normal (ULN) with the following exception: patients with known Gilbert disease who have serum bilirubin level =\< 3 x ULN may be enrolled (obtained within 4 weeks \[+/-3 days\] prior to study entry). * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 3.0 x ULN (obtained within 4 weeks \[+/-3 days\] prior t…