Inclusion Criteria:

          -  Patients with recurrent squamous cell carcinoma or a second primary arising in a
             previously irradiated field

          -  Life expectancy of greater than 6 months

          -  Patients cannot have distant metastases and have to be candidates for curative
             re-irradiation

          -  Patients with salivary gland tumors are excluded (patients with nasopharynx or
             sinonasal cancers can participate)

          -  Patients with unresectable disease are eligible

          -  Patients who undergo surgical resection will be allowed regardless of human papilloma
             virus (HPV) status provided they have one of the following criteria:

               -  Positive margins on pathology

               -  Evidence of extracapsular spread on nodal pathology

               -  Gross residual disease on postoperative or simulation imaging

               -  N2/3 disease

               -  T3/4 disease

               -  Multifocal perineural invasion and/or lymphovascular space invasion

          -  The majority of the anticipated target volume (> 50%) must have been previously
             treated to ≥ 40 Gy; prior radiation therapy (RT) must have been completed > 6 months
             prior to initiation of IMRT reirradiation; if previous RT records are unavailable,
             investigators can estimate the dose to previously treated tissues based on completion
             notes or other treatment history

          -  An Eastern Cooperative Oncology Group (ECOG) performance score 0-2

          -  Granulocytes > 1500/mm³

          -  Platelets > 100,000/mm³

          -  Bilirubin < 1.5 mg/dl

          -  Creatinine < 1.5 mg/dl

          -  No other concurrent invasive malignancies treated for the past year (localized
             prostate cancer or early stage skin cancer are not exclusion criteria)

          -  Patients with carotid artery involvement or encasement will be allowed provided they
             have no symptoms related to carotid involvement

          -  No prior exposure to immunotherapy agents

          -  Ability to understand and the willingness to sign a written informed consent document

        Exclusion Criteria:

          -  Any known factors that would pose a contraindication to receiving nivolumab

          -  Recursive partitioning analysis (RPA) class III patients defined as those expected to
             begin reirradiation within 2 years of first course of radiation therapy AND are
             percutaneous endoscopic gastrostomy (PEG) dependent or have a tracheostomy (patients
             who have undergone total laryngectomy are not excluded)

          -  Patients with metastases

          -  Prior treatment with a programmed cell death protein-1 (PD-1)/programmed death-ligand
             1 (PD-L1) inhibitor

          -  Female patients of childbearing potential must have a negative serum pregnancy test
             within 7 days prior to enrollment

          -  Patients with primary salivary gland cancers are excluded

          -  Patients who have had chemotherapy or biological therapy within 4 weeks of
             registration

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, autoimmune disease requiring systemic steroids, symptomatic congestive
             heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric
             illness/social situations that would limit compliance with study requirements

          -  Patients who are pregnant or breast-feeding

          -  Patients with known active human immunodeficiency virus (HIV), hepatitis (hep) B, or
             hep C infection

          -  Subjects with a 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