Everolimus, Erlotinib Hydrochloride, and Radiation Therapy in Treating Patients With Recurrent Head and Neck Cancer Previously Treated With Radiation Therapy

Inclusion Criteria: * Recurrent aerodigestive cancers of squamous cell histology of the head and neck, or those who have a second head and neck primary cancer, who have received prior radiation therapy for a head and neck malignancy with curative intent * Patients must locally advanced disease, without distant metastases; measurable disease as per Response Evaluation Criteria In Solid Tumors (RECIST) is not required * Patients who had surgery for recurrent disease or a second primary in a previously radiated field are eligible if their surgical pathology specimen from the resection exhibits high risk features such as positive margins or extracapsular extension * Patient may have more than one recurrence as long as the current recurrence occurs at least \>= 6 months after the end of prior radiation therapy * Only one prior course of radiotherapy to the head and neck region is allowed; prior chemotherapy is allowed * Based on prior radiation treatment records, most (\> 50%) of the tumor volume must have been in areas previously irradiated to \>= 45 Gy without exceeding spinal cord tolerance (combining previous and future radiation dose to the spinal cord of =\< 50 Gy) * The previous total radiation dose must not have exceeded a maximum dose of 75 Gy * Karnofsky Performance Status \> 70 or Eastern Cooperative Oncology Group (ECOG) Performance Status 0-1 * Patients must sign study-specific informed consent and Health Insurance Portability and Accountability Act (HIPAA) forms * P…