I. Pharmacodynamic (PD) biomarker response: PARP inhibition in peripheral blood mononuclear cells (PBMC) by measurement of PAR levels. (ORIGINAL DOSE ESCALATION PORTION) II. DNA damaging effects of irinotecan and the combination of irinotecan with ABT-888: levels of gamma H2A histone family, member X (gamma-H2AX) and RAD51 recombinase (Rad51) formation in tumor tissue. (ORIGINAL DOSE ESCALATION PORTION) III. Relevance of cytochrome P450 family 2, subfamily C, polypeptide 9 (CYP2C9) and 2C19 polymorphisms, uridine 5'-diphosphosphate (UDP) glucuronosyltransferase 1 family, polypeptide A1 (UGT1A1) polymorphism, and ATP-binding cassette, sub-family G (WHITE), member 2 (ABCG2) polymorphism to the pharmacokinetics of irinotecan and/or ABT-888. (ORIGINAL DOSE ESCALATION PORTION) IV. To explore whether a positive gamma-H2AX response in tumor tissue at 4-6 hours (hrs) is reflected in circulating tumor cells (CTCs) between 8-24 hrs but not at 4-6 hrs, as predicted. (EXPANSION PORTION) V. To explore whether PARP inhibition increases gamma-H2AX response of CTCs to plasma drug by 4-6 hrs after CPT-11 administration. (EXPANSION PORTION) VI. To explore whether PARP inhibition increases gamma-H2AX response of tumor cells to tissue drug level, as indicated by CTCs at 8-24 hrs after CPT-11. (EXPANSION PORTION) VII. To explore when the gamma-H2AX response peak in CTCs occurs, indicating a response in tumor. (EXPANSION PORTION) VIII. To explore whether there is a tumor switch between gamma-H2AX and excision repair cross-complementation group 1 (ERCC1)-mediated repair in the presence of PARP inhibition, (i.e., repeat initial PBMC and tumor findings). (EXPANSION PORTION) IX. To perform analysis of CTCs at day 15 to help guide alteration in ABT-888 drug administration schedule (continuous administration). (EXPANSION PORTION) X. To sequence the genome and transcriptome from both normal and tumor tissue from each study patient in the expansion cohort to evaluate point mutations, structural changes and copy number events. (EXPANSION PORTION) XI. To evaluate the damaging effects of irinotecan and the combination of irinotecan with ABT-888 by examining levels of Rad51 formation in tumors. (EXPANSION PORTION) XII. To evaluate the percentage of breast cancer stem cells (BCSC) in serial breast tumor biopsies before and after irinotecan alone and after 1 cycle of treatment with the combination of irinotecan and ABT-888. (EXPANSION PORTION) XIII. To perform molecular profiling of the tumor cell and BCSC populations before and after irinotecan alone and after 1 cycle of treatment with the combination of irinotecan and ABT-888. (EXPANSION PORTION) XIV. To compare Rad51 foci in aldehyde dehydrogenase-positive (ALDH+) stem cell populations to the bulk tumor cells. (EXPANSION PORTION) XV. To develop assays to detect trapping of PARP1 and 2 in tumor biopsy tissue in response to treatment with irinotecan plus a PARP inhibitor, in this case ABT-888. (DOSE ESCALATION FOR INTERMITTENT ABT-888 PORTION) XVI. Additional exploratory assay to be named later. (DOSE ESCALATION FOR INTERMITTENT ABT-888 PORTION) XVII. To determine the tumor response as assessed by the Response Evaluation Criteria in Solid Tumors (RECIST) in an expansion cohort of 12 triple-negative breast cancer (BRCA)-mutant breast cancer patients.