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 institut…