Guadecitabine and Durvalumab in Treating Patients With Advanced Liver, Pancreatic, Bile Duct, or Gallbladder Cancer

Inclusion Criteria: * Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L (\> 1500 per mm\^3) except for patients with HCC for whom ANC \>= 1000 per mm\^3 is allowed * Platelet count \>= 100 x 10\^9/L (\> 100,000 per mm\^3), except for patients with HCC for whom a platelet count \> 60,000 per mm\^3 is allowed * Hemoglobin \>= 8.0 g/dL; if patients have a hemoglobin level below 8, blood transfusion is allowed to meet the eligibility criteria as long as post transfusion hemoglobin is maintained at \>= 8.0 g/dL for 7 days or longer * Aspartate aminotransferase (AST)/serum glutamic-oxaloacetic transaminase (SGOT) and alanine aminotransaminase (ALT)/serum glutamate pyruvate transaminase (SGPT) =\< 2.5 x institutional upper limit of normal unless liver metastases are present or unless patient is known to have chronic liver disease (hepatitis) in which case AST and ALT must be =\< 5 x institutional upper limit of normal (IULN) * Serum bilirubin =\< 2.5 x institutional upper limit of normal (ULN) * Serum albumin \>= 2.5 g/dL * Serum creatinine clearance (CL) \> 40 mL/min by the Cockcroft-Gault formula or by 24-hour urine collection for determination of creatinine clearance * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 90 days foll…