Stereotactic Body Radiation Therapy in Treating Patients With High Risk Locally Advanced Head and Neck Cancer

Inclusion Criteria: * The participant must have squamous cell carcinoma proven by histologic diagnosis; for cancers of the oropharynx, p16 staining by immunohistochemistry must be negative; for cancers of the larynx, hypopharynx, oral cavity, nasopharynx, paranasal sinuses, p16 staining is not required * The participant must have clinical stage T1-4, N0-3, M0-1, stage II-IVC carcinoma as per the 7th edition of the American Joint Committee on Cancer (AJCC) staging manual; participants with T1N0M0 will be ineligible; participants with metastatic disease with a limited metastatic burden are eligible if obtaining local control is determined by their treating oncologist to be an important therapeutic goal * The participant must have imaging documenting a primary tumor, or involved lymph node, ≥ 2.5 cm in greatest dimension * PET/CT is required for all participants, unless contraindicated; this may be acquired prior to study entry or after enrollment prior to SBRT planning * The participant must have a history and physical documented within four weeks of registration and be deemed by a medical oncologist to be ineligible for standard continuous course chemoradiotherapy with cisplatin * Karnofsky performance status (PS) ≥ 40 * Female participants cannot be of childbearing age, or if they are, must have a negative pregnancy test prior to enrollment and be willing to use contraceptives during treatment and continue for 6 additional months * Participants must have the ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Participants with T1N0M0 stage I disease * Participants who are receiving any other investigational agents * Participants with non-squamous cell histology * Participants with life expectancy \< 6 months * Participants who cannot lie flat for 20 minutes * Participants with prior history of head and neck radiotherapy (\> 40 Gy) with significant areas of anticipated overlap