Inclusion Criteria:

• Ability to understand and the willingness to sign a written informed consent document
• Histologically or cytologically confirmed non-keratinizing nasopharyngeal carcinoma (NPC) that has recurred at locoregional and/or distant sites; NOTE: patients with local recurrence at the bony skull-base as the only site of index disease are excluded; patients with locoregional recurrence without distant metastases must have undergone radical radiotherapy previously
• Measurable disease according to the RECIST criteria (version 1.1), for the evaluation of measurable disease
• Received one or more lines of chemotherapy, which must include prior treatment with a platinum agent and must not be amenable to potentially curative radiotherapy or surgery
• Archived or fresh tumor sample available; willingness to donate blood and tissue for mandatory correlative research studies
• Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2
• Absolute neutrophil count ≥ 1.5 x 10^9/L
• Platelet count ≥ 100 x 10^9/L
• Hemoglobin ≥ 8.0 g/dL
• Serum alanine aminotransferase ([ALT]; serum glutamate-pyruvate transferase [SGPT]), or serum aspartate aminotransferase [AST] where available at the center) < 2.5 x upper limit of normal (ULN), OR < 5 x ULN in the presence of liver metastases
• Serum total bilirubin < 2 x ULN (except patients with Gilbert syndrome, who can have total bilirubin < 3.0 mg/dL)
• Serum creatinine < 1.5 x ULN

Exclusion Criteria:

• Any of the following:
  • Chemotherapy ≤ 4 weeks prior to registration
  • Radiotherapy ≤ 4 weeks prior to registration
  • Nitrosoureas ≤ 6 weeks prior to registration or
  • Mitomycin C ≤ 6 weeks prior to registration
  • Those who have not recovered from adverse events (to grade ≤ 1 in severity) due to agents administered more than 4 weeks earlier; prior palliative radiotherapy to bone metastases ≤ 2 weeks prior to registration (i.e. prior palliative radiotherapy to bone metastases is allowed if it is performed > 2 weeks prior to registration)
• Prior investigational agents ≤ 4 weeks prior to registration
• Prior treatment with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-cytotoxic T-lymphocyte antigen 4 (CTLA-4) antibody, or any other antibody or drug specifically targeting T-cell co-stimulation or immune checkpoint pathways
• Known brain metastases or leptomeningeal metastases; NOTE: symptomatic, and/or if they require immunosuppressive doses of corticosteroids (e.g. > 10 mg/day prednisone or equivalents) for at least 2 weeks prior to study drug administration; patients with treated brain metastases who are deemed clinically stable and without radiological progression on positron emission tomography (PET), MRI or computed tomography (CT) scan performed ≤ 8 weeks of study entry, are not excluded; NOTE: primary nasopharyngeal cancers that directly invade the skull base and extend into the infratemporal fossa (e) are not regarded as brain metastases and are not excluded
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to nivolumab
• History of severe hypersensitivity reaction to any monoclonal antibody
• Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
• Any of the following:
  • Pregnant women
  • Nursing women
  • Men or women of childbearing potential who are unwilling to employ adequate contraception
    NOTE: breastfeeding should be discontinued if the mother is treated with nivolumab; women of childbearing potential and men must use two forms of contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; they must adhere to contraception for a period of 31 weeks after the last dose of nivolumab
• For patients with unknown human immunodeficiency virus (HIV) status at the time of enrollment, HIV serology must be tested during screening; patients who are tested positive for HIV could be included if there is an adequate cluster of differentiation 4 (CD4) count (> 350/ul) on a stable regimen of highly active anti-retroviral therapy (HAART) with no detectable or minimal viral burden, and no active infections
• For patients with unknown hepatitis B virus surface antigen (HbsAg) status, must be tested during study screening; patients who are tested positive test for HBsAg are excluded if they have inadequately controlled hepatitis B and/or Child-Pugh Class B or C cirrhosis; however, patients with adequately controlled hepatitis are not excluded from the study if they satisfy all of the following criteria: (i) must be receiving a nucleoside analog anti-viral drug for 3 or more months; and (ii) have a serum hepatitis B virus (HBV) deoxyribonucleic acid (DNA) level of less than 100 IU/ml via polymerase chain reaction quantification assays prior to enrollment
• For patients with unknown hepatitis C virus ribonucleic acid (HCV RNA) status, must be tested during study screening; patients who are tested positive for HCV RNA are excluded from the study if they have inadequately controlled hepatitis C and/or Child-Pugh Class B or C cirrhosis; patients with adequately controlled hepatitis are not excluded from the study as defined by having undetectable level of serum HCV RNA level prior to enrollment; patients who are currently on interferon or other anti-HCV therapy will be excluded from study
• Active autoimmune disease or history of autoimmune disease that might recur, which may affect vital organ function or require immune suppressive treatment including systemic corticosteroids; NOTE: these include but are not limited to patients with a history of immune related neurologic disease, multiple sclerosis, autoimmune (demyelinating) neuropathy, Guillain-Barre syndrome, myasthenia gravis; systemic autoimmune disease such as systemic lupus erythematosus (SLE), connective tissue diseases, scleroderma, inflammatory bowel disease (IBD), Crohn's, ulcerative colitis, hepatitis; and patients with a history of toxic epidermal necrolysis (TEN), Stevens-Johnson syndrome, or phospholipid syndrome should be excluded; patients with vitiligo, endocrine deficiencies including thyroiditis managed with replacement hormones including physiologic corticosteroids are eligible; patients with rheumatoid arthritis and other arthropathies, Sjögren's syndrome and psoriasis controlled with topical medication and patients with positive serology, such as antinuclear antibodies (ANA), anti-thyroid antibodies should be evaluated for the presence of target organ involvement and potential need for systemic treatment but should otherwise be eligible
• Patients are permitted to enroll if they have vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger (precipitating event)
• Condition requiring systemic treatment with either corticosteroids (> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration; inhaled or topical steroids and adrenal replacement doses ≤ 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease; patients are permitted to use topical, ocular, intra-articular, intranasal, and inhalational corticosteroids (with minimal systemic absorption); physiologic replacement doses of systemic corticosteroids are permitted, even if ≤ 10 mg/day prednisone equivalents; a brief course of corticosteroids for prophylaxis (e.g., contrast dye allergy) or for treatment of non-autoimmune conditions (e.g., delayed-type hypersensitivity reaction caused by contact allergen) is permitted
• Evidence of active or acute (i.e. current, or recent within 4 weeks prior to registration) diverticulitis, intra-abdominal abscess, gastrointestinal (GI) obstruction and abdominal carcinomatosis which are known risk factors for bowel perforation; patients with abdominal carcinomatosis, a history of non-recent intra-abdominal abscess, or a history of non-recent GI obstruction should be evaluated for the potential need for additional treatment before coming on study