Testing the Addition of an Anti-cancer Drug, Adavosertib, to Radiation Therapy for Patients With Incurable Esophageal and Gastroesophageal Junction Cancers

Inclusion Criteria: * Patients must have histologically confirmed esophageal cancer (either squamous cell or adenocarcinoma), including Siewert gastroesophageal junction adenocarcinomas types 1 and 2, that is inoperable and not eligible for definitive chemoradiation after multidisciplinary review or have pathologically confirmed or imaging consistent with metastatic disease * Age \>= 18 years. Because no dosing or adverse event data are currently available on the use of AZD1775 in combination with radiation therapy in patients \< 18 years of age, children are excluded from this study * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 (Karnofsky \>= 70%) * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Hemoglobin \>= 9 g/dL * Platelets \>= 100,000/mcL * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x institutional ULN * Creatinine =\< 1.5 x institutional ULN OR * Glomerular filtration rate (GFR) \>= 60 mL /min/1.73 m\^2 unless data exists supporting safe use at lower kidney function values, no lower than 30 mL/min/1.73 m\^2 * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated * Patients with a history of hepatitis C virus (HCV) infection must have bee…