• Patients must have a histologically confirmed NUT carcinoma that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective.

• Patient may be treatment naïve or have had prior surgery, radiation, or any systemic therapy (with the exceptions noted in the Exclusion Criteria).

• Patients must have histologically or cytologically confirmed NUT carcinoma based on the ectopic expression of NUT protein per World Health Organization (WHO) criteria as determined by immunohistochemistry (IHC) and/or detection of NUT gene translocation as determined by fluorescence in situ hybridization (FISH) at a Clinical Laboratory Improvement Act (CLIA) certified laboratory and/or by detection of the NUT gene translocation as determined by sequencing (e.g., deoxyribonucleic acid \[DNA\] next generation sequencing \[NGS\] or ribonucleic acid \[RNA\] sequencing) at a CLIA certified laboratory.

• Patients must have measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) v.1.1.

• Patients must be age ≥ 18 years.

• Patients must exhibit an Eastern Cooperative Oncology Group (ECOG) performance status of 0-2.

• Leukocytes (WBC) ≥ 3,000/mcL.

• Absolute neutrophil count (ANC) ≥ 1,500/mcL.

• Hemoglobin (Hgb) ≥ 9 g/dL.

• Platelets (PLT) ≥ 100,000/mcL.

• Total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN).

• Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) ≤ 3 x institutional ULN.

• Alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) ≤ 3 x institutional ULN.

• Creatinine ≤ 1.5 x institutional ULN.

• Glomerular filtration rate (GFR) ≥ 40 mL/min/1.73 m\^2.

⁃ Estimated (e)GFR is estimated GFR calculated by the abbreviated Modification of Diet in Renal Disease (MDRD) equation.

• Patients with treated brain metastases are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression.

• Patients with new or progressive brain metastases (active brain metastases) or leptomeningeal disease are eligible if the treating physician determines that immediate CNS specific treatment is not required and is unlikely to be required during the first cycle of therapy.

• The effects of cemiplimab on the developing human fetus are unknown. For this reason and because immune checkpoint inhibitor agents as well as other therapeutic agents used in this trial are known to be teratogenic, patients of child-bearing potential (POCBP) and their partners with sperm-producing reproductive capacity must agree to use adequate contraception from time of informed consent, for the duration of study participation, and for 6 months following completion of cemiplimab therapy. Should a POCBP become pregnant or suspect they are pregnant while they or their partner are participating in this study, they should inform their treating physician immediately.

⁃ NOTE: A POCBP is any patient (regardless of gender, sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) with an egg-producing reproductive tract who meets the following criteria:

∙ Has not undergone a hysterectomy or bilateral oophorectomy

‣ Has had menses at any time in the preceding 12 consecutive months (and therefore has not been naturally postmenopausal for \> 12 months)

• POCBP must have a negative pregnancy test prior to registration on study.

• Patients with sperm-producing reproductive capacity (PWSPRC) treated or enrolled on this protocol must also agree to use adequate contraception with partners of childbearing potential from time of informed consent, for the duration of study participation, and for 6 months after completion of administration.