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 following completion of therapy; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * A female of child-bearing potential is any woman (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) who meets the following criteria: * Has not undergone a hysterectomy or bilateral oophorectomy; or * Has not been naturally postmenopausal for at least 12 consecutive months (i.e., has had menses at any time in the preceding 12 consecutive months) * Female subjects must either be of non-reproductive potential (ie, post-menopausal by history: \>= 60 years old and no menses for \>= 1 year without an alternative medical cause; OR history of hysterectomy, OR history of bilateral tubal ligation, OR history of bilateral oophorectomy) or must have a negative serum pregnancy test upon study entry * Ability to understand a written informed consent * Signed written informed consent and Health Insurance Portability and Accountability Act (HIPAA) obtained from the subject prior to performing any protocol-related procedures, including screening evaluations * Subject is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations including follow up * Patients must have measurable disease as defined by RECIST 1.1 criteria * Hepatocellular carcinoma cohort specific criteria: * Patients must have a histologically proven diagnosis of hepatocellular carcinoma that is not amenable to curative surgical therapeutic options * Patients must not be good candidates for locoregional therapy as determined by the investigator (ie diffuse multifocal disease, vascular involvement, etc) * Patients must have had evidence of radiologic progression on sorafenib or have had intolerance to sorafenib as defined by the recurrence of clinically significant toxicities despite a minimum of one dose reduction and appropriate supportive care; patients who refuse sorafenib are eligible with documentation of refusal by the treating physician * Patients may have received other treatment for HCC such as embolization, chemoembolization, intra-arterial chemotherapy, ethanol injection, ablative therapy, cryosurgery, or other locoregional or targeted therapy * Patients must have a Child Pugh score of 7 points or less * International normalized ratio (INR) =\< 2.3 or prothrombin time =\< 6 seconds above control * Patients with hepatitis B infection must be on appropriate anti-viral therapy * Cholangiocarcinoma cohort specific criteria: * Patients must have histologically or cytologically documented carcinoma primary to the intra- or extra-hepatic biliary system or gall bladder with clinical and/or radiologic evidence of unresectable, locally advanced or metastatic disease; patients with ampullary carcinoma are not eligible * Patients must have failed at least one (but no more than 2) prior line of systemic therapy in the advanced disease setting * Patients who received adjuvant chemotherapy and had evidence of disease recurrence within 6 months of completion of the adjuvant treatment are also eligible; in this case, the adjuvant therapy will count as the minimum required one prior line of therapy; if patient received adjuvant treatment and had disease recurrence after 6 months, patients will only be eligible after failing one regimen of systemic chemotherapy used to treat the (unresectable or metastatic) disease recurrence * If the patient has had decompression of the biliary tree within the last 14 days, stability of the bilirubin level needs to be confirmed with two measurements that are within 5 to 7 days of each other; (the second measurement must be obtained within 7 days prior to registration); both the first and second measurement must be =\< 2.5 x IULN; stability is defined as the second measurement being no more than one point higher than the first * Pancreatic cancer cohort specific criteria: * Patients must have unresectable or metastatic pancreatic cancer * Patients must have failed at least one prior line of therapy for metastatic or unresectable disease or have recurred within 6 months of completing adjuvant chemotherapy * Patients with liver metastases must have \< 50% involvement of the liver Exclusion Criteria: * Patients may not be receiving any other investigational agents * Patients must not be nursing due to the potential for congenital abnormalities and the potential of this regimen to harm nursing infants * Any previous treatment with a hypomethylating agent, or with a PD1 or PD-L1 or anti-PD-L2 or anti-CTLA4 inhibitor, including durvalumab (or any other antibody or drug specifically targeting T-cell costimulation or checkpoint pathways); any immunomodulatory agent that is not described above should be cleared by the principal investigator (PI) * History of another primary malignancy except for: * Malignancy treated with curative intent and with no known active disease \>= 3 years before the first dose of study drug * Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease * Adequately treated carcinoma in situ without evidence of disease eg, cervical cancer in situ * Controlled, superficial bladder carcinoma * T1a or T1b or T1c prostate carcinoma treated with radiation \>= 1 year prior to study enrollment and prostate specific antigen (PSA) within normal limits (WNL) since treatment * T2a or b prostate carcinoma treated curatively \>= 1 year prior to study enrollment and PSA undetectable since curative treatment * Other early stage cancers that have a minimal chance of recurrence (i.e stage I endometrial cancer, cervical cancer, etc.) may be cleared by the PI * Receipt of the last dose of anti-cancer therapy (chemotherapy, immunotherapy, endocrine therapy, targeted therapy, biologic therapy, tumor embolization, monoclonal antibodies, other investigational agent) within 28 days prior to the first dose of study drug and within 6 weeks for nitrosourea or mitomycin C * Mean QT interval corrected for heart rate (QTc) \>= 470 ms calculated from 3 electrocardiograms (ECGs) using Fridericia?s correction * Current or prior use of immunosuppressive medication within 28 days before the first dose of durvalumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed 10 mg/day of prednisone, or an equivalent corticosteroid; live attenuated vaccines within 30 days of durvalumab dosing (ie, 30 days prior to the first dose, during treatment with durvalumab and for 30 days post discontinuation of durvalumab); inactivated vaccines, such as the injectable influenza vaccine, are permitted * Any unresolved toxicity Common Terminology Criteria for Adverse Events (CTCAE) grade 2 or more from previous anti-cancer therapy, except alopecia, hearing loss, peripheral neuropathy or non-clinically significant laboratory abnormalities * Any prior grade \>= 3 immune-related adverse event (irAE) while receiving any previous immunotherapy agent, or any unresolved irAE \> grade 1 * Active or prior documented autoimmune disease; subjects with vitiligo, Grave?s disease, or psoriasis not requiring systemic treatment (within the past 2 years) are not excluded * Active or prior documented inflammatory bowel disease (e.g., Crohn?s disease, ulcerative colitis) * History of primary immunodeficiency * History of allogeneic organ transplant * History of hypersensitivity to durvalumab, guadecitabine (SGI-110) or any excipient * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, uncontrolled hypertension (defined as systolic blood pressure(SBP) \> 160 or diastolic blood pressure (DBP) \> 100 on 2 separate occasions separated by at least 24 hours), unstable angina pectoris, cardiac arrhythmia, active peptic ulcer disease or gastritis, active bleeding diathesis including any subject known to have evidence of human immunodeficiency virus (HIV), or psychiatric illness/social situations that would limit compliance with study requirements or compromise the ability of the subject to give written informed consent * Known history of previous clinical diagnosis of tuberculosis * History of leptomeningeal carcinomatosis or uncontrolled seizures * Receipt of live attenuated vaccination within 30 days prior to study entry or within 30 days of receiving durvalumab * Any condition that, in the opinion of the investigator, would interfere with evaluation of study treatment or interpretation of patient safety or study results * Symptomatic or uncontrolled brain metastases requiring concurrent treatment, inclusive of but not limited to surgery, radiation and/or corticosteroids * Presence of ascites that is not medically controlled or that required a therapeutic paracentesis within the last 3 months prior to initiation of study therapy * Known history or ongoing diagnosis of pneumonitis * Hepatocellular carcinoma cohort specific exclusion criteria: * A history of hepatic encephalopathy within the past 12 months; patients on stable doses of lactulose for prophylaxis or as a result of previous hepatic encephalopathy (more than 12 months ago) are allowed (for HCC cohort only) * A history of bleeding esophageal or gastric varices within the last 6 months prior to initiation of study therapy