Trifluridine/Tipiracil and Irinotecan for the Treatment of Advanced Refractory Biliary Tract Cancer

Inclusion Criteria: * Histological confirmation of advanced biliary tract cancers including cancers originating in the gallbladder who have received at least one line of systemic anticancer therapy * Note: Patients who have either progressed on or are intolerant to the prior therapy can be included in this study * Measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) criteria * NOTE: Tumor lesions in a previously irradiated area are not considered measurable disease. Disease that is measurable by physical examination only is not eligible * Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0 or 1 * Absolute neutrophil count (ANC) \>= 1500/mm\^3 (=\< 21 days prior to registration) * Platelet count \>= 100,000/mm\^3 (=\< 21 days prior to registration) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) (=\< 21 days prior to registration) * Aspartate transaminase (AST) or alanine transaminase (ALT) =\< 3 x ULN (=\< 21 days prior to registration) * Creatinine =\< 1.5 x ULN (=\< 21 days prior to registration) * Negative pregnancy test done =\< 7 days prior to registration, for persons of childbearing potential only * Provide written informed consent * Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study) * Willingness to provide mandatory blood and tissue specimens for correlative research Exclusion Criteria: * Any of the following because this study involves an age…