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 * Patient must be willing to have percutaneous endoscopic gastrostomy (PEG) placement if necessary * Patients must be able to swallow oral medications * Patients and/or their partners of childbearing potential are required to use adequate birth control during and for 6 months after completion of study therapy * Leukocytes \>= 3,000/ul * Absolute neutrophil count \>= 1,500/ul * Platelets \>= 100,000/ul * Total bilirubin =\< institutional upper limit of normal * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.5 x institutional upper institutional limits * OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Hemoglobin \>= 9 g/dL * Fasting serum cholesterol =\< 300 mg/dL OR =\< 7.75 mmol/L; AND fasting triglycerides =\< 2.5 x upper limit of normal (ULN); NOTE: In case one or both of these thresholds are exceeded, the patient can only be included after initiation of appropriate lipid lowering medication at any point prior to the initiation of therapy * International normalized ratio (INR) =\< 1.5; (anticoagulation is allowed if target INR =\< 1.5 on a stable dose of warfarin or on a stable dose of low molecular weight \[LMW\] heparin for \> 2 weeks at time of randomization) Exclusion Criteria: * Patient has history of using erlotinib or any other EGFR inhibitors (prior C225/Cetuximab treatment is allowed if given with radiation therapy, but treatment must have been completed at least 6 months prior to study entry) * Patient has history of receiving RAD001 or any other mTOR inhibitors * Patient is known to be allergic to any type of EGFR tyrosine kinase inhibitors or mTOR inhibitors * Patients receiving chronic, systemic treatment with corticosteroids or another immunosuppressive agent; topical or inhaled corticosteroids are allowed * As judged by the investigator, any evidence of severe or uncontrolled psychiatric or systemic disease (e.g., unstable or uncompensated respiratory, cardiac, hepatic, or renal disease); history of noncompliance to medical regimens * Pregnant or breast-feeding women or adults of reproductive potential who are not using effective birth control methods; adequate contraception must be used throughout the trial and for 8 weeks after the last dose of study drug, by both sexes; (women of childbearing potential must have a negative urine or serum pregnancy test within 7 days prior to administration of RAD001) * Concomitant use of phenytoin, carbamazepine, rifampicin, barbiturates, or St John's Wort; these medications can be discontinued one week prior to enrollment if medically feasible * Treatment on any other clinical protocols or with a non-approved or investigational drug within 4 weeks before Day 1 of study treatment * Any evidence of clinically active interstitial lung disease (patients with chronic stable radiographic changes who are asymptomatic need not be excluded) * Known active connective tissue disorders, such as lupus or scleroderma which, in the opinion of the treating physician, may put the patient at high risk for radiation toxicity * Patients with known human immunodeficiency virus (HIV) infection and/or acquired immune deficiency (AIDS) * Patients with known multiple sclerosis * Patients with nasopharyngeal carcinoma are excluded; other malignancies within the past 3 years which actively require ongoing treatment except for treated carcinoma of the cervix or basal or squamous cell carcinomas of the skin * Patients should not receive immunization with attenuated live vaccines within one week of study entry or during study period; close contact with those who have received attenuated live vaccines should be avoided during treatment with RAD001; examples of live vaccines include intranasal influenza, measles, mumps, rubella, oral polio, Bacillus Calmette-Guerin (BCG), yellow fever, varicella and TY21a typhoid vaccines * Patients who have any severe and/or uncontrolled medical conditions or other conditions that could affect their participation in the study such as: * Symptomatic congestive heart failure of New York heart Association Class III or IV * Unstable angina pectoris, symptomatic congestive heart failure, myocardial infarction =\< 6 months of start of study drug, serious uncontrolled cardiac arrhythmia or any other clinically significant cardiac disease * Severely impaired lung function as defined as spirometry and diffusion capacity of carbon monoxide (DLCO) that is 50% of the normal predicted value and/or oxygen (O2) saturation that is 88% or less at rest on room air * Uncontrolled diabetes as defined by fasting serum glucose \> 1.5 x ULN * Active (acute or chronic) or uncontrolled severe infections * Liver disease such as cirrhosis, chronic active hepatitis or chronic persistent hepatitis; Note: A detailed assessment of hepatitis B/C medical history and risk factors must be done at screening for all patients; hepatitis B virus (HBV) deoxyribonucleic acid (DNA) and hepatitis C virus (HCV) ribonucleic acid (RNA) polymerase chain reaction (PCR) testing are required at screening for all patients with a positive medical history based on risk factors and/or confirmation of prior HBV/HCV infection * Steroid or supplemental oxygen required for exacerbations of chronic obstructive lung disease * Impairment of gastrointestinal function or gastrointestinal disease that may significantly alter the absorption of RAD001 (e.g., ulcerative disease, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome or small bowel resection) * Current active smokers are excluded; these patients may be enrolled if they report that they have refrained from smoking for a minimum of 7 days * Patients with an active, bleeding diathesis * Patients, who have had a major surgery or significant traumatic injury within 4 weeks of start of study drug, patients who have not recovered from the side effects of any major surgery (defined as requiring general anesthesia) or patients that may require major surgery during the course of the study