Combination of Carboplatin, Eribulin and Veliparib in Stage IV Cancer Patients

Inclusion Criteria: * Patients must have archival biopsy specimens (preferably from metastatic disease) available for research tests. If a suitable biopsy specimen is not available, patients will be asked to undergo a research biopsy to procure tissue * Patients must be \>/= 18 years * Females of childbearing potential must not have had unprotected sexual intercourse within 30 days prior to study entry and must agree to use a highly effective method of contraception. Females who are using hormonal contraceptives must have been on a stable dose of the same hormonal contraceptive product for at least 4 weeks prior to dosing and must continue to use the same contraceptive during the study and for 30 days after study drug discontinuation * Patients must have an ECOG performance status 0-1 * Patients may have had a prior diagnosis of cancer if it has been \> 5 years since their last treatment for that cancer * Patients must have normal organ and marrow function as defined below: * Leukocytes ≥ 3,000/uL * Absolute neutrophil count ≥ 1,500/uL * Platelets ≥ 100,000/uL * Creatinine within normal limits or creatinine clearance ≥30 * Patients must be able to swallow and retain oral medication * Patients who were receiving prior systemic therapy: Prior treatment related side effects must have resolved to \< Grade 2 severity (except alopecia and infertility) * All patients must have given signed, informed consent prior to registration on study * Patients must have stage IV breast or stage III and IV ovarian cancer (including platinum sensitive disease) * Patients must have BRCA1/2 deleterious mutations, PTEN deficiency, or cancer with a high HRD score as assessed by Myriad's assay * Patients must have measurable disease per RECIST 1.1 criteria (see above for definition) * Patients may not have received more than 3 chemotherapeutic regimens for metastatic disease * Patients may not have received treatment with prior carboplatin, eribulin or a PARP inhibitor Exclusion Criteria: * Women who are pregnant or lactating are not eligible * Patients who are undergoing concomitant radiotherapy are not eligible * Patients who are receiving any other investigational agents or concurrent anticancer therapy are not eligible * Previous systemic treatment is allowed with a 21 day washout period prior to registration * Patients who are taking any herbal (alternative) medicines are not eligible. Patients must be off any such medications by the time of registration * Patients with known brain metastases are not eligible for participation unless the following are met: * Brain metastases are treated (either with surgical excision, stereotactic radiosurgery or radiotherapy and have been stable for at least 4 weeks (MRI documented) * Patient is asymptomatic and has discontinued corticosteroids if taken for that purpose * Patients with any of the following conditions or complications are NOT eligible for participation: * GI tract disease resulting in an inability to take oral medication * Malabsorption syndrome * Require IV alimentation * History of prior surgical procedures affecting absorption * Uncontrolled inflammatory GI disease (e.g., Crohn's, ulcerative colitis). * Hypersensitivity of any of the components of Veliparib, carboplatin, eribulin * History of significant neurological (no neuropathy \> Grade 2) or psychiatric disorders. * Significant non-neoplastic liver disease (e.g., cirrhosis, active chronic hepatitis). * Significant non-neoplastic renal disease. * Immunocompromised subjects, including subjects known to be infected with human immunodeficiency virus (HIV). * Uncontrolled endocrine diseases (e.g., diabetes mellitus, hypothyroidism or hyperthyroidism, adrenal disorder) i.e., requiring relevant changes in medication within the last month or hospital admission within the last three months * Active infection requiring systemic therapy. * Significant cardiovascular impairment: history of congestive heart failure greater than New York Heart Association (NYHA) Class II, uncontrolled arterial hypertension, unstable angina, myocardial infarction or stroke within 6 months of the first dose of study drug; or cardiac arrhythmia requiring medical treatment. * Prolongation of QTc interval to \> 480 msec when electrolytes balance is normal. * Major surgery within 4 weeks prior to the first dose of study drug