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 to study entry). * Alkaline phosphatase =\< 2.5 x ULN with the following exception: patients with documented bone metastases: alkaline phosphatase =\< 5 x ULN (obtained within 4 weeks \[+/-3 days\] prior to study entry). * Serum creatinine =\< 1.5 x ULN or creatinine clearance \>= 50 mL/min on the basis of the Cockcroft-Gault glomerular filtration rate estimation (obtained within 4 weeks \[+/-3 days\] prior to study entry). * Measurable disease per RECIST v1.1 and/or per direct clinical measurements for primary tumors upon a variance between clinical and radiographic evaluation. * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * International normalized ratio (INR) and activated partial thromboplastin time (aPTT) =\< 1.5 x ULN (This applies only to patients who do not receive therapeutic anticoagulation; patients receiving therapeutic anticoagulation \[such as low-molecular-weight heparin or warfarin\] should be on a stable dose.) * No evidence of distant metastases and measurable disease (\> 1.5 cm). * Please Note: Patients may be enrolled regardless of their language. The ICD / translator SOP will be followed for Non-English speaking patients. Cognitively-Impaired adults may be considered for this protocol. If so, the ICD / LAR SOP will be followed. Exclusion Criteria: * Any approved anticancer therapy, including chemotherapy, hormonal therapy, or radiotherapy, within 3 weeks prior to initiation of study treatment; however, the following are allowed: Hormone-replacement therapy; palliative radiotherapy for bone metastases \> 2 weeks prior to cycle 1, day 1. * Adverse events (AEs) from prior anticancer therapy that have not resolved to grade =\< 1 except for alopecia. * Bisphosphonate therapy for symptomatic hypercalcemia * Use of bisphosphonate therapy for other reasons (e.g., osteoporosis) is allowed. * Patients with acute leukemias, accelerated/blast phase chronic myelogenous leukemia, chronic lymphocytic leukemia, Burkitt lymphoma, plasma cell leukemia, or non-secretory myeloma. * Pregnancy, lactation, or breastfeeding. * Known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies. * Inability to comply with study and follow-up procedures. * History or risk of autoimmune disease, including but not limited to systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjogren's syndrome, Bell's palsy, Guillain-Barre syndrome, multiple sclerosis, autoimmune thyroid disease, vasculitis, or glomerulonephritis. Patients with a history of autoimmune hypothyroidism on a stable dose of thyroid replacement hormone may be eligible. Patients with controlled type 1 diabetes mellitus on a stable insulin regimen may be eligible. * Patients with eczema, psoriasis, lichen simplex chronicus of vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis would be excluded) are permitted provided that they meet the following conditions: Patients with psoriasis must have a baseline ophthalmologic exam to rule out ocular manifestations; Rash must cover less than 10% of body surface area (BSA); Disease is well controlled at baseline and only requiring low potency topical steroids (e.g., hydrocortisone 2.5%, hydrocortisone butyrate 0.1%, fluocinolone 0.01%, desonide 0.05%, alclometasone dipropionate 0.05%); No acute exacerbations of underlying condition within the last 12 months (not requiring psoralen plus ultraviolet A radiation \[PUVA\], methotrexate, retinoids, biologic agents, oral calcineurin inhibitors; high potency or oral steroids). * History of idiopathic pulmonary fibrosis, pneumonitis (including drug induced), organizing pneumonia (i.e., bronchiolitis obliterans, cryptogenic organizing pneumonia, etc.), or evidence of active pneumonitis on screening chest computed tomography (CT) scan. * History of radiation pneumonitis in the radiation field \[fibrosis\] is permitted. * Any other diseases, metabolic dysfunction, physical examination finding, or clinical laboratory finding giving reasonable suspicion of a disease or condition that contraindicates the use of an investigational drug or that may affect the interpretation of the results or render the patient at high risk from treatment complications. * History of human immunodeficiency virus (HIV) infection or active hepatitis B (chronic or acute) or hepatitis C infection. * Patients with past or resolved hepatitis B infection; defined as having a negative hepatitis B surface antigen (HBsAg) test and a positive anti-HBc (antibody to hepatitis B core antigen) antibody test, are eligible. * Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA). * Active tuberculosis. * Severe infections within 4 weeks prior to cycle 1, day 1, including but not limited to hospitalization for complications of infection, bacteremia, or severe pneumonia. * Signs or symptoms of infection as determined by the treating team within 2 weeks prior to cycle 1, day 1. * Received oral or IV antibiotics within 2 weeks prior to cycle 1, day 1 * Patients receiving prophylactic antibiotics (e.g., for prevention of a urinary tract infection or chronic obstructive pulmonary disease) are eligible. * Major surgical procedure within 28 days prior to cycle 1, day 1. * Administration of a live, attenuated vaccine within 4 weeks before cycle 1, day 1 or anticipation that such a live, attenuated vaccine will be required during the study. * Influenza vaccination should be given during influenza season only (approximately October to March). Patients must not receive live, attenuated influenza vaccine (e.g., FluMist) within 4 weeks prior to cycle 1, day 1 or at any time during the study. * Malignancies other than the disease under study within 5 years prior to cycle 1, day 1, with the exception of those with a negligible risk of metastasis or death and with expected curative outcome (such as adequately treated carcinoma in situ of the cervix, basal or squamous cell skin cancer, localized prostate cancer treated surgically with curative intent, or ductal carcinoma in situ treated surgically with curative intent) or undergoing active surveillance per standard-of-care management (e.g., chronic lymphocytic leukemia Rai Stage 0, prostate cancer with Gleason score =\< 6, and prostate-specific antigen \[PSA\] =\< 10 mg/mL, etc.) * Continued sexual activity in men\*\* or women of childbearing potential\*\*\* who are unwilling to practice highly effective contraception during the study and until 6 months after the last dose of study drug (highly effective contraceptive measures include stable use of oral contraceptives such as combined estrogen and progestogen and progestogen only hormonal contraception or other prescription pharmaceutical contraceptives for 2 or more menstrual cycles prior to screening; intrauterine device \[IUD\]; intrauterine hormone-releasing system \[IUS\]; bilateral tubal ligation; vasectomy, and sexual abstinence). (\*\*Contraception is not required for men with documented vasectomy \*\*\*Postmenopausal women must be amenorrheic for at least 12 months in order not to be considered of childbearing potential. Pregnancy testing and contraception are not required for women with documented hysterectomy or tubal ligation.) * Prior treatment with anti-PD-1, or anti-PD-L1 therapeutic antibody or pathway targeting agents. Patients who have received prior treatment with anti-CTLA-4 may be enrolled, provided the following requirements are met: Minimum of 12 weeks from the first dose of anti-CTLA-4 and \> 6 weeks from the last dose. No history of severe immune-related adverse effects from anti-CTLA 4 (National Cancer Institute \[NCI\] Common Terminology Criteria for Adverse Events \[CTCAE\] grade 3 and 4). * Treatment with systemic immunostimulatory agents (including but not limited to interferon \[IFN\] or interleukin \[IL\]-2) within 6 weeks or five half-lives of the drug (whichever is shorter) prior to cycle 1, day 1. * Treatment with investigational agent within 4 weeks prior to cycle 1, day 1 (or within five half lives of the investigational product, whichever is longer). * Treatment with systemic immunosuppressive medications (including but not limited to prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor \[anti-TNF\] agents) within 2 weeks prior to cycle 1, day 1. * Patients who have received acute, low dose, systemic immunosuppressant medications (e.g., a one-time dose of dexamethasone for nausea) may be enrolled. * The use of inhaled corticosteroids and mineralocorticoids (e.g., fludrocortisone) for patients with orthostatic hypotension or adrenocortical insufficiency is allowed. * History of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins. * Patients with prior allogeneic bone marrow transplantation or prior solid organ transplantation. * Patients with prior treatment with idelalisib.