Veliparib, Cisplatin, and Vinorelbine Ditartrate in Treating Patients With Recurrent and/or Metastatic Breast Cancer

Inclusion Criteria: * Recurrent and/or metastatic breast cancer * Subjects must meet at least one of the following two criteria: * Histologically confirmed primary or metastatic site that is estrogen receptor (ER)-negative (less than 10%), progesterone receptor (PR)-negative (less than 10%), and human epidermal growth factor receptor (HER)2 non-over expressing by immunohistochemistry (IHC) (0, 1) or non-amplified by fluorescence in situ hybridization (FISH) * Confirmed BRCA1 or BRCA2 mutation associated breast cancer * Subjects must have measurable disease, defined as at least one lesion that can be measured in at least one dimension with a minimum size of: longest diameter \>= 10 mm (computed tomography \[CT\] scan slice thickness no greater than 5 mm); 10 mm caliper measurement by clinical exam; to be considered pathologically enlarged and measurable, a lymph node must be \>= 15 mm in short axis when assessed by CT scan * Subjects may have had any number of prior chemotherapy, endocrine therapy, immunologic, or biologic regimens for metastatic breast cancer * Performance status \>= 60% on the Karnofsky scale (Eastern Cooperative Oncology Group \[ECOG\] =\< 2) * Absolute neutrophil count (ANC) \>= 1,500/mm\^3 (1.5 x 10\^9/L) * Platelets \>= 100,000/mm\^3 (100 x 10\^9/L) * Hemoglobin \>= 9.0 g/dL * Serum creatinine =\< 1.5 x upper normal limit of institution's normal range OR creatinine clearance \>= 50 mL/min/1.73 m\^2 for subjects with creatinine levels above institutional normal * Aspartate aminotransferase (AST) and/or alanine aminotransferase (ALT) =\< 2.5 x the upper normal limit of institution's normal range; for subjects with liver metastases, AST and/or ALT \< 5 x the upper normal limit of institution's normal range * Bilirubin =\< 1.5 x the upper normal limit of institution's normal range; subjects with Gilbert's syndrome may have a bilirubin \> 1.5 x the upper normal limit of institution's normal range * Partial thromboplastin time (PTT) must be =\< 1.5 x the upper normal limit of institution's normal range and international normalized ratio (INR) \< 1.5; subjects on anticoagulant (such as Coumadin) will have PTT and INR as determined by the investigator * Women of childbearing potential must agree to use adequate contraception (one of the following listed below) prior to study entry, for the duration of study participation and for 90 days following completion of therapy; women of childbearing potential must have a negative serum pregnancy test within 21 days prior to initiation of treatment and/or be confirmed as having postmenopausal status; criteria for determining menopause include any of the following: prior bilateral oophorectomy; age \>= 60 years; age \< 60 years and amenorrheic for at least 12 months in the absence of chemotherapy, endocrine therapy, or ovarian suppression and follicle-stimulating hormone (FSH) and estradiol in the postmenopausal range; * Total abstinence from sexual intercourse (minimum one complete menstrual cycle) * Vasectomized partner of female subjects * Hormonal contraceptives (oral, parenteral or transdermal) for at least 3 months prior to study drug administration * Double-barrier method (condoms, contraceptive sponge, diaphragm or vaginal ring with spermicidal jellies or cream) * Intra-uterine device (IUD) * Male subjects (including those who are vasectomized) whose partners are pregnant or might be pregnant must agree to use condoms for the duration of the study and for 90 days following completion of therapy * Radiation therapy of a non-target lesion must have been completed at least 2 weeks prior to the enrollment date * Subjects with known brain metastases must have clinically controlled neurologic symptoms, defined as surgical excision and/or radiation therapy followed by 14 days of stable neurologic function prior to the first dose of study drug * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Subject has received any anti-cancer therapy including chemotherapy, immunotherapy, biologic or any investigational therapy within either 28 days or 5 half-lives of a targeted therapy (whichever is shorter), prior to study drug administration; subjects receiving hormone therapy, bisphosphonates, denosumab or luteinizing-hormone-releasing hormone (LHRH)-agonists are eligible; subjects who have not recovered to within one grade level (not to exceed grade 2) of their baseline following a significant adverse event or toxicity attributed to prior anti-cancer treatment are excluded * Subjects with a known hypersensitivity to platinum compounds or vinorelbine * Subjects with baseline peripheral neuropathy that exceeds grade 1 * Clinically significant and uncontrolled major medical condition(s) including but not limited to: * Active uncontrolled infection * Symptomatic congestive heart failure * Unstable angina pectoris or cardiac arrhythmia * Psychiatric illness/social situation that would limit compliance with study requirements * Any medical condition, which in the opinion of the study investigator, places the subject at an unacceptably high risk for toxicities * Subjects with significant fluid retention, including ascites or pleural effusion, may be allowed at the discretion of the principal investigator * Subject is pregnant or lactating