Inclusion Criteria:
* 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.
Exclusion Criteria:
* Patients must have the ability to understand and the willingness to sign a written informed consent document prior to the start of any study activities (e.g. before screening/baseline activities and before registration on the study) and comply with the study requirements.
* Prior treatment with PD-1 or PD-L1 inhibitors.
* Received systemic therapy, radiation, or had surgery ≤ 14 days prior to planned treatment start date.
* NOTE: Prior therapy must meet requirements of criteria listed in Exclusion Criteria
* Patients who have not recovered from adverse events due to prior anti-cancer therapy, (i.e., have residual toxicities \> grade 1 per National Cancer Institute \[NCI\] Common Terminology Criteria for Adverse Events \[CTCAE\] v5) with the exception of alopecia, neuropathy, and other non-significant adverse events.
* Patients who are receiving any investigational agents or devices ≤ 14 days from planned start of treatment date.
* History of allergic reactions or acute hypersensitivity reactions attributed to compounds of similar chemical or biologic composition to immune checkpoint inhibitors and/or to antibody treatments.
* Patients with a known history of Human immunodeficiency virus (HIV).
* NOTE: Infected patients on effective anti-retroviral therapy with an undetectable viral load for 6 months prior to start of study participation are eligible to participate.
* NOTE: CD4+ T cell counts and viral load are monitored per standard of care.
* Patients with a known history of chronic hepatitis B virus (HBV) infection.
* NOTE: Patients with HBV and an undetectable viral load on suppressive therapy are eligible to participate.
* NOTE: CD4+ T cell counts, and viral load are monitored per standard of care.
* Patients with a known history of hepatitis C virus (HCV) infection.
* NOTE: For patients with a known HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load OR
* NOTE: Patients with an HCV infection must have been treated and cured in order to participate.
* NOTE: CD4+ T cell counts, and viral load are monitored per standard of care.
* Patients who have an uncontrolled intercurrent illness including, but not limited to any of the following:
* Hypertension that is not controlled on medication
* Ongoing or active infection requiring systemic treatment
* NOTE: Prophylactic antibiotic treatment is allowed (e.g. for uncomplicated infections such as urinary tract infections \[UTIs\] or sinus infections being treated with oral antibiotics)
* Symptomatic congestive heart failure
* Unstable angina pectoris
* Cardiac arrhythmia
* History of pneumonitis within the last 5 years
* Any other illness or condition that the treating investigator feels would interfere with study compliance or would compromise the patient's safety or study endpoints.
* Patients with psychiatric illness/social situations that would limit compliance with study requirements.
* Patients have received a prior allogeneic stem cell transplant or received an organ transplant.
* Patients have ongoing or recent (within 5 years) evidence of significant autoimmune disease that required treatment with systemic immunosuppressive treatments, which may suggest risk for immune mediated adverse events (imAEs).
* NOTE the following are not exclusionary:
* Vitiligo,
* Childhood asthma that has resolved,
* Type 1 diabetes,
* Residual hypothyroidism that required only hormone replacement,
* Psoriasis that does not require systemic treatment.
* And the following medications:
* Intranasal, inhaled, topical steroids, or local steroid injections (e.g., intra-articular injection);
* Systemic corticosteroids at physiologic doses ≤ 10 mg/day of prednisone or equivalent;
* Steroids as premedication for hypersensitivity reactions (e.g., CT scan premedication).
* Patients that received prior treatment with other immune modulating agents that was:
* Less than 4 weeks (28 days) prior to the first dose of cemiplimab, or
* Associated with imAEs that were grade ≥ 1 within 90 days prior to the first dose of cemiplimab, or
* Associated with toxicity that resulted in discontinuation of the immune-modulating agent.
* Patients of child-bearing potential (POCBP) who are pregnant or nursing.
* NOTE: POCBP that are pregnant or are nursing are excluded from this study; cemiplimab is an immune checkpoint inhibitor agent with potential for teratogenic or abortifacient effect. There is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with cemiplimab; breastfeeding should be discontinued if the patient is a nursing parent treated with cemiplimab.
* Patient with a current or prior malignancy within the previous 2 years and in the opinion of the treating investigator would interfere with monitoring of radiological assessments of response to cemiplimab. Exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or in situ cervical cancer that has undergone potentially curative therapy. Incidentally diagnosed prostate cancer is also allowed if assessed as stage ≤ T2N0M0 and Gleason score ≤ 6.
