Trifluridine/Tipiracil and Talazoparib for the Treatment of Patients With Locally Advanced or Metastatic Colorectal or Gastroesophageal Cancer

Inclusion Criteria: * Histologically or cytologically confirmed CRC or EGC adenocarcinoma that is locally advanced or metastatic (Cohort A); histologically or cytologically confirmed p53mt/RASonc (Cohort B1) or p53mt/RASwt CRC (Cohort B2) that is locally advanced or metastatic. Patients with adenocarcinoma histology only are allowed to participate. * Has received at least one prior line of therapy with progression or intolerance * Have measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria present * Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * Life expectancy \>= 3 months by investigator assessment * Hemoglobin \>= 9 g/dL * Absolute neutrophil count \>= 1500/mm\^3 * Platelet count \>= 100,000/mm\^3 without transfusion or growth factor support * Creatinine \< 1.5 upper limit of normal (ULN) or creatinine clearance \> 60 mL/min * Total bilirubin \< 1.5 x ULN * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.5 x ULN or \< x 5 ULN in the presence of liver metastasis * Albumin \> 3 g/dL * Ability to swallow oral medications * Participants of child-bearing potential must agree to use adequate contraceptive methods (e.g., hormonal or barrier method of birth control; abstinence) prior to study entry. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately * Participant must understand…