This phase II trial studies how well stereotactic body radiation therapy or intensity modulated radiation/proton therapy works in treating patients with head and neck cancer that has come back. Stereotactic body radiation therapy uses special equipment to position a patient and deliver radiation to tumors with high precision. This method can kill tumor cells with fewer doses over a shorter period and cause less damage to normal tissue. Intensity modulated radiation/proton therapy uses high energy x-rays or protons to kill tumor cells and shrink tumors. It is not yet known whether stereotactic body radiation therapy or intensity modulated radiation/proton therapy may work better in treating patients with head and neck cancer.

PRIMARY OBJECTIVES: I. To compare the 2-year rate of Common Terminology Criteria for Adverse Events (CTCAE)-4.0 grade 3 or higher toxicity at 2 years between the two treatment arms. SECONDARY OBJECTIVES: I. To compare the 2-year locoregional failure free survival (LFFS) in patients being treated with reirradiation with either stereotactic ablative radiotherapy (SBRT) versus intensity modulated radiation therapy/intensity modulated proton therapy (IMRT/IMPT). II. To determine if there is any difference in local control, progression-free survival, and overall survival between the two arms. III. To compare toxicity using Common Terminology Criteria for Adverse Events (CTCAE)-4.0 and Performance Status Scale-HN (Head and Neck). IV. To compare patient reported outcome (PRO) measures of symptoms using MD Anderson Symptom Inventory (MDASI), MD Anderson Dysphagia Inventory (MDADI), Functional Assessment of Cancer Therapy (FACT)-HN, ACT-HN Symptom Index (FACT-HNSI), MD Anderson Symptom Inventory-Brain Tumor (MDASI-BT), for skull base only, Anterior Skull BASE Questionnaire (ASBQ), for skull base only, Brief Fatigue Inventory (BFI), Telephone Interview for Cognitive Status (TICS), Performance Status Scale For Head and Neck Cancer Patients (PSS-HN), Work Productivity and Activity Impairment Questionnaire: Specific Health Problem version (V)2.0 (WPAI:SHP), and University of Michigan Xerostomia-Related Quality of Life Scale, Xerostomia and Health Questionnaire (European Quality of Life Five Dimension Three Level \[EQ-5D-3L\]). V. Quality-Adjusted-Life-Years (QALY) comparison between IMPT and IMRT. VI. Compare cost-benefit economic analysis of treatment. VII. Perform dosimetric analysis and compare correlates of critical structures. EXPLORATORY OBJECTIVES: I. To assess potential differences between patients on study and patients who were considered eligible for randomized, were randomized to a treatment arm, but may have dropped out of the study for other reasons after being randomized to; or were denied insurance coverage for the treatment arm she/he was randomized. OUTLINE: Patients are randomized into 1 of 2 groups. GROUP I: Patients undergo SBRT every other day for a total of 5 treatments. GROUP II: Patients undergo IMRT/IMPT once daily (Monday-Friday) for up to 30-35 treatments. After completion of study treatment, patients are followed up at 2-3 months, every 3 months for 1 year, and then every 3-4 months for up to 2 years.