Olaparib in Treating Patients With Metastatic Biliary Tract Cancer With Aberrant DNA Repair Gene Mutations

Inclusion Criteria: * Age \>= 18 years * Histological or cytological documentation of metastatic adenocarcinoma of the biliary tract * Patients with previously identified genetic aberrations that are associated with homologous recombinant repair pathway will be eligible \[e.g. somatic mutations in ATM, ATR, CHEK2, BRCA 1/2, RAD51, BRIP1, PALB2, PTEN, FANC, NBN, EMSY, MRE11, ARID1A\] or germline mutations in the above genes. Clinical Laboratory Improvement Act (CLIA)-certified assays including commercial tests (Foundation Medicine, Caris, Tempus) will be allowed * Measurable disease * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0 to 2. (Form is available on the Academic and Community Cancer Research United \[ACCRU\] website) * Life expectancy of \>= 16 weeks per estimation of investigator * Absolute neutrophil count (ANC) \>= 1500/mm\^3 (obtained =\< 7 days prior to registration) * Platelet count \>= 75,000/mm\^3 (obtained =\< 7 days prior to registration) * Hemoglobin \>= 9.0 g/dL with no blood transfusion in the past 28 days (obtained =\< 7 days prior to registration) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) (obtained =\< 7 days prior to registration) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x ULN (=\< 5 x ULN for subjects with liver involvement of their cancer) (obtained =\< 7 days prior to registration) * Serum creatinine =\< 1.5 x ULN (obtained =\< 7 days prior to registration) * Institutional norm…