Testing the Addition of the Anti-cancer Viral Therapy Telomelysin™ to Chemoradiation for Patients With Advanced Esophageal Cancer and Are Not Candidates for Surgery

Inclusion Criteria: * Pathologically (histologically or cytologically) proven diagnosis of adenocarcinoma or squamous cell carcinoma (SCC) of the esophagus or gastroesophageal junction (GEJ) within 90 days prior to registration * Gastroesophageal junction tumors must be Siewert type I/II * Required diagnostic workup for study entry: * History/physical examination prior to registration * Computed tomography (CT) of the chest/abdomen with intravenous contrast within 28 days prior to registration; If CT contrast is contraindicated magnetic resonance imaging (MRI) of the chest/abdomen without contrast is permitted * Bronchoscopy for squamous cell carcinoma (SCC) tumors that are adjacent to the airway to exclude a tracheoesophageal fistula within 42 days prior to registration * Endoscopic ultrasound (if technically feasible) within 90 days prior to registration * Whole body positron emission tomography (PET)/CT scan within 42 days prior to registration: Note: scan will be used for radiation treatment planning, in addition to ruling out metastatic disease * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 within 14 days prior to registration * Adequate hematologic function within 14 days prior to registration defined as follows Absolute neutrophil count ≥ 1,500/mcL (within 14 days prior to registration) Hemoglobin ≥ 9 gm/dL (within 14 days prior to registration) Platelets ≥ 100,000/mcL (within 14 days prior to registration) * Adequate renal functio…