Erlotinib Hydrochloride in Treating Patients With Advanced Esophageal Cancer or Stomach Cancer

Inclusion Criteria: * Histologically or cytologically confirmed adenocarcinoma, squamous cell or small cell carcinoma, or carcinoma not otherwise specified of the esophagus or gastroesophageal junction * Metastatic or surgically unresectable disease * Measurable disease outside of primary tumor * At least 20 mm by conventional techniques OR at least 10 mm by spiral computed tomography (CT) scan * No bone metastases, abnormal radionuclide bone scans, or pleural effusions as only site of measurable disease * No known brain metastases or carcinomatous meningitis * Must consent to having tumor tissue tested for epidermal growth factor receptor status * Performance status-Karnofsky 70-100% * Life expectancy of greater than 3 months * Absolute neutrophil count at least 1,500/mm\^3 * Platelet count at least 100,000/mm\^3 * Bilirubin no greater than 2 times upper limit of normal (ULN) * Aspartate aminotransferase (AST) no greater than 2 times ULN * Creatinine no greater than 1.5 mg/dL * Calcium no greater than 12 mg/dL * No symptomatic hypercalcemia * No symptomatic congestive heart failure * No unstable angina pectoris * No ventricular arrhythmia * No other malignancy within the past 3 years except adequately treated carcinoma in situ of the cervix, superficial transitional cell carcinoma of the bladder, or basal cell or squamous cell skin cancer * No other uncontrolled concurrent illness * No ongoing or active infection * No psychiatric illness or social situation that would preclude study participation * No other concurrent disease that would preclude study participation * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No prior cetuximab * No more than 1 prior chemotherapy regimen for advanced or metastatic disease * One prior chemotherapy in the adjuvant setting (in combination with prior surgery or radiotherapy) allowed provided it was administered prior to treatment for advanced or metastatic disease * At least 3 weeks since prior chemotherapy * No concurrent investigational or commercial chemotherapy * At least 3 weeks since prior radiotherapy * No prior erlotinib-related compounds or compounds of similar biologic or chemical components * No prior EGFR-targeting compounds (e.g., gefitinib) * No other concurrent investigational agents * No concurrent combination antiretroviral therapy for human immunodeficiency virus (HIV)-positive patients