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 limit of normal (ULN), OR: Creatinine clearance \>= 50 mL/min according to Cockcroft Gault formula or other institutional methods * Patients must have a corrected QT interval by Fridericia (QTcF) =\< 480 msec * International normalized ratio (INR) =\< 1.5 and no clinically significant bleeding event within the past six months * Ability to understand and the willingness to sign a written informed consent document * Patients must have measurable disease, per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * The effects of birinapant on the developing human fetus are unknown. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) beginning at study entry and for the duration of study participation. Male study participants should use an additional barrier method of contraception for 30 days following the last dose of birinapant. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately Exclusion Criteria: * Eligibility for curative-intent surgery, unless the patient is considered a poor surgical candidate related to resectability, functional outcome, or prefers non-surgical therapy * More than 2 lines of palliative systemic therapy (platinum-, taxane- or cetuximab-based chemotherapy or immunotherapy) * Patients who are receiving any other investigational agents * Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events * History of allergic reactions attributed to compounds of similar chemical or biologic composition to birinapant * 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 * Pregnant women are excluded from this study because birinapant may have potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with birinapant, breastfeeding should be discontinued prior to enrollment. A negative pregnancy test is required for women of childbearing potential. Women who are postmenopausal (age-related amenorrhea \>= 12 consecutive months, or who had undergone hysterectomy or bilateral oophorectomy are exempt from pregnancy testing. If necessary, to confirm postmenopausal status, a follicle stimulating hormone (FSH) level may be included at screening * Human immunodeficiency virus (HIV) positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with birinapant * Patients requiring the use of anti-tumor necrosis factor (anti TNF) therapies, such as infliximab, or patients who have received treatment with anti-TNF therapies within 5 half-lives of the drug (48 days for infliximab, 55 days for golimumab, 70 days for certolizumab and adalimumab, and 16 days for etanercept) * Patients with previous exposure to birinapant