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 normalized ratio (INR)/activated partial thromboplastin time (aPTT) =\< 1.5 x ULN (obtained =\< 7 days prior to registration) * Exception: Patients who are therapeutically treated with anticoagulant agents will be allowed to participate provided that no prior evidence of underlying abnormality in coagulation parameters exists. Close monitoring of at least weekly evaluations will be performed until INR/PTT is stable based on a measurement that is pre-dose as defined by the local standard of care * Alkaline phosphatase limit =\< 2.5 x ULN (=\< 5 x ULN for patients with liver involvement of their cancer) (obtained =\< 7 days prior to registration) * Creatinine clearance estimated of \>= 51 mL/min using the Cockcroft-Gault equation (obtained =\< 7 days prior to registration) * Negative serum pregnancy test done =\< 28 days prior to registration and confirmed prior to treatment on day 1, for women of childbearing potential, postmenopausal women or women of childbearing potential with evidence of non-childbearing status. * Postmenopausal is defined as: * Amenorrheic for 1 year or more following cessation of exogenous hormonal treatments * Luteinizing hormone (LH) and follicle stimulating hormone (FSH) levels in the post-menopausal range for women under 50 * Radiation-induced oophorectomy with last menses \> 1 year ago * Chemotherapy-induced menopause with \> 1 year interval since last menses * Surgical sterilization (bilateral oophorectomy or hysterectomy) * Provide informed written consent * Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study) * Willing to provide blood and tissue for correlative purposes * Hepatitis B virus surface antigen (HBsAg), anti-hepatitis B virus core antigen (anti-HBc) and hepatitis B virus surface antigen (anti-HBs) * Patients with chronic HBV receiving any systemic anticancer therapy should receive antiviral prophylactic therapy through and for minimum 12 months following anticancer therapy * Patients with past HBV undergoing other systemic anticancer therapies not clearly associated with a high risk of HBV reactivation should be monitored with HBsAg and alanine aminotransferase during cancer treatment (suggest every other cycle) Exclusion Criteria: * Platinum refractory disease which was defined as: * Evidence disease progression on platinum based chemotherapy regimen or * Evidence of disease progression =\< 6 months of completion of platinum based adjuvant chemotherapy regimen * Patient has received prior systemic anti-cancer therapy, tumor embolization or radiotherapy =\< 28 days prior to registration * Major surgical procedure, open biopsy, or significant traumatic injury =\< 28 days prior to registration * NOTE: Patients must have recovered from any effects of any major surgery * Congestive heart failure - New York Heart Association (NYHA) \>= class II * Resting electrocardiogram (ECG) indicating uncontrolled, potentially reversible cardiac conditions, as judged by the investigator (eg. unstable ischemia, uncontrolled symptomatic arrhythmia, corrected QT interval by Fridericia's correction formula \[QTcF\] prolongation \> 500 ms, electrolyte disturbances, etc.), or patients with congenital long QT syndrome. Cardiac arrhythmias requiring anti-arrhythmic therapy. * NOTE: Pacemaker, beta blockers or digoxin are permitted * Uncontrolled hypertension - grade 3 or higher per Common Terminology Criteria for Adverse Events (CTCAE) version (v) 5.0. (despite optimal medical management) * History of or current pheochromocytoma * Arterial or venous thrombotic or embolic events such as cerebrovascular accident (including transient ischemic attacks), deep vein thrombosis or pulmonary embolism =\< 6 months prior to registration * Ongoing infection \> grade 2 National Cancer Institute (NCI)-Common Terminology Criteria for Adverse Events (CTCAE) version (v)5.0 * Seizure disorder requiring medication * Symptomatic metastatic brain or meningeal tumors unless the patient is \> 6 months from definitive therapy, has a negative imaging study =\< 28 days of registration and is clinically stable with respect to the tumor at the time of registration. Patients with spinal cord compression unless considered to have received definitive treatment for this and evidence of clinically stable disease for 28 days prior to registration * NOTE: The patient can receive a stable dose of corticosteroids before and during the study as long as these were started =\< 28 days prior to registration * History of organ allograft (including corneal transplant) or allogenic bone marrow transplant or double umbilical cord blood transplantation (dUCBT) * Evidence or history of bleeding diathesis or any hemorrhage or bleeding event \> CTCAE v5.0 grade 3, =\< 28 days prior to registration * Non-healing wound, ulcer, or bone fracture * Renal failure requiring hemo-or peritoneal dialysis * Dehydration CTCAE v5.0 grade \>= 2 * Substance abuse, medical, psychological or social conditions that may interfere with the patient's participation in the study or evaluation of the study results * Known hypersensitivity to any of the study drugs, study drug classes, or excipients in the formulation * Interstitial lung disease with ongoing signs and symptoms at the time of informed consent * Persistent proteinuria of CTCAE v5.0 grade 3 or higher (\>= 3.5 g/24 hours \[hrs\]) * Unable to swallow orally administered medications * Any malabsorption condition and/or patients with gastrointestinal disorders likely to interfere with absorption of the study medication * Unresolved toxicity greater than CTCAE v5.0 grade 2 attributed to any prior therapy/procedure excluding alopecia and oxaliplatin induced neurotoxicity =\< grade 2 * Albumin levels \< 2.5 g/dl * Any of the following because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown. * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception * NOTE: Women of childbearing potential and their partners, who are sexually active, must agree to the use of TWO highly effective forms of contraception in combination. This should be started from the time of registration and continue throughout the period of taking study treatment and for at least 1 month after last dose of study drug(s), or they must totally/truly abstain from any form of sexual intercourse. * Male patients must use a condom during treatment and for 3 months after the last dose of olaparib when having sexual intercourse with a pregnant woman or with a woman of childbearing potential. Female partners of male patients should also use a highly effective form of contraception if they are of childbearing potential. Male patients should not donate sperm throughout the period of taking olaparib and for 3 months following the last dose of olaparib * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens. Patients considered a poor medical risk due to a serious, uncontrolled medical disorder, non-malignant systemic disease or active, uncontrolled infection. Examples include, but are not limited to, uncontrolled ventricular arrhythmia, recent (within 3 months) myocardial infarction, uncontrolled major seizure disorder, unstable spinal cord compression, superior vena cava syndrome, extensive interstitial bilateral lung disease on high resolution computed tomography (HRCT) scan or any psychiatric disorder that prohibits obtaining informed consent * Immunocompromised patients and patients known to be human immunodeficiency virus (HIV) serologically positive and currently receiving antiretroviral therapy. * NOTE: Patients known to be HIV positive, but without clinical evidence of an immunocompromised state, are eligible for this trial * Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm * Previous and/or intercurrent cancers. With the exception of: curatively-treated cancers with no recurrence in \>= 5 years or early cancers treated with curative intent, including but not limited to cervical carcinoma in situ, superficial, noninvasive bladder cancer, basal cell carcinoma, squamous cell carcinoma in situ, ductal carcinoma in situ (DCIS), Stage 1, grade 1 endometrial carcinoma, or endoscopically resected gastrointestinal cancers limited in mucosal layer * NOTE: All cancer treatments for cancers that were distinct in a primary site other than biliary tract cancer must be completed \>= 3 years prior to registration * Pleural effusion or ascites that causes respiratory compromise (\>= CTCAE v5.0 grade 2 dyspnea) * Previous enrollment in the present study * Prior exposure to any PARP inhibitor including olaparib * Known hypersensitivity reaction to olaparib or any of the excipients of the product * Myelodysplastic syndrome/acute myeloid leukemia or with features suggestive of myelodysplastic syndrome/acute myeloid leukemia (MDS/AML) * Concomitant use of known strong CYP3A inhibitors (eg. itraconazole, telithromycin, clarithromycin, protease inhibitors boosted with ritonavir or cobicistat, indinavir, saquinavir, nelfinavir, boceprevir, telaprevir) or moderate CYP3A inhibitors (eg. ciprofloxacin, erythromycin, diltiazem, fluconazole, verapamil). * NOTE: The required washout period prior to registration is 2 weeks * Concomitant use of known strong (eg. phenobarbital, enzalutamide, phenytoin, rifampicin, rifabutin, rifapentine, carbamazepine, nevirapine and St John's Wort) or moderate CYP3A inducers (eg. bosentan, efavirenz, modafinil). * NOTE: The required washout period prior to registration is 5 weeks for enzalutamide or phenobarbital and 3 weeks for other agents * Patient taking medications or herbal products including grapefruits, grapefruit hybrids, pomelos, star fruits, Seville oranges, pomegranates, or the juice from any of these. Note: Patients must discontinue the drug/product \>= 7 days prior to registration * Patient taking medications with a known risk to prolong the QTc interval and/or cause Torsades de Pointes. Note: Patients must be discontinued \>= 7 days of registration. Treating physicians may wish to replace the drug(s) that do not carry this risk with safe alternative(s) * Whole blood transfusions in the last 120 days prior to entry to the study (packed red blood cells and platelet transfusions are acceptable outside of 28 days prior to treatment) * Involvement in the planning and/or conduct of the study * Judgment by the investigator that the patient should not participate in the study if the patient is unlikely to comply with study procedures, restrictions and requirements