Birinapant and Intensity Modulated Re-Irradiation Therapy in Treating Patients With Locally Recurrent Head and Neck Squamous Cell Carcinoma

Inclusion Criteria: * Patients must have histologically or cytologically confirmed locally recurrent HNSCC, including nasopharyngeal or sinonasal cancer for whom re-irradiation for local control is considered standard of care * Patients with human papillomavirus (HPV)-negative or HPV-positive head and neck cancer are eligible * Patients who have had prior treatment with immune therapies are eligible * Patients must have received curative-intent platinum- and/or cetuximab-based chemoradiotherapy or radiotherapy alone * Patients must have completed their last treatment dose with chemotherapy or immunotherapy at least 4 weeks (6 weeks for nitrosoureas or mitomycin C) before enrolling on study * Patients must have completed their last treatment dose with radiotherapy at least 6 months before enrolling on study * Patients who have had major surgery must be fully recovered and require a recovery period of at least 4 weeks prior to enrolling on study * Age \>= 18 years * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Hemoglobin \>= 9 g/dL (transfusion permitted) * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin within 1.5 x the upper limit of normal (ULN) institutional limits * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal * Serum creatinine =\< 1.5 x upper limi…