Inclusion Criteria:

* Patients must have recurrent or persistent epithelial ovarian, fallopian tube, or primary peritoneal carcinoma AND carry a germline mutation in BRCA1 or BRCA2 (confirmation required via Myriad test report); histologic documentation of the original primary tumor is required via the pathology report
* All patients must have measurable disease as defined by Response Evaluation Criteria in Solid Tumors(RECIST)1.1; measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded); each lesion must be \>= 10 mm when measured by computed tomography (CT), magnetic resonance imaging (MRI), or caliper measurement by clinical exam; or \>= 20 mm when measured by chest x-ray; lymph nodes must be \>= 15 mm in short axis when measured by CT or MRI
* Patient must have at least one "target lesion" to be used to assess response on this protocol as defined by RECIST; tumors within a previously irradiated field will be designated as "non-target" lesions unless progression is documented or a biopsy is obtained to confirm persistence at least 90 days following completion of radiation therapy
* Patients who have received one prior cytotoxic regimen must have a Gynecological Oncology Group (GOG) performance status of 0, 1, or 2
* Patients who have received two or three prior cytotoxic regimens must have a GOG performance status of 0 or 1
* Recovery from effects of recent surgery, radiotherapy, or chemotherapy

* Patients should be free of active infection requiring antibiotics (with the exception of uncomplicated urinary tract infection \[UTI\])
* Any hormonal therapy directed at the malignant tumor must be discontinued at least one week prior to registration; continuation of hormone replacement therapy is permitted
* Any other prior therapy directed at the malignant tumor, including chemotherapy, biologic/targeted (non-cytotoxic) agents and immunologic agents, must be discontinued at least three weeks prior to registration; patients receiving nitrosoureas or mitomycin C must discontinue 6 weeks prior to registration
* Any prior radiation therapy must be discontinued at least four weeks prior to registration
* Prior therapy

* Patients must have had one prior platinum-based chemotherapeutic regimen for management of primary disease containing carboplatin, cisplatin, or another organoplatinum compound; this initial treatment may have included intraperitoneal therapy, consolidation, biologic/targeted (non-cytotoxic) agents or extended therapy administered after surgical or non-surgical assessment
* Patients are allowed to receive, but are not required to receive, two additional cytotoxic regimens for management of recurrent or persistent disease
* Patients are allowed to receive, but are not required to receive, biologic/targeted (non-cytotoxic) therapy for management of recurrent or persistent disease; patients are allowed to receive, but are not required to receive, biologic/targeted (non-cytotoxic) therapy as part of their primary treatment regimen
* Patients with both platinum-sensitive and platinum-resistant disease are eligible; patients with platinum-refractory disease are NOT eligible
* Definitions:

* Platinum sensitive ovarian cancer is defined as patients who respond to platinum-based therapy (complete or partial) and then progress/recur more than 6 months after their last platinum dose (i.e., platinum-free interval is \> 6 months)
* Platinum resistant ovarian cancer is defined as patients who respond to platinum-based therapy (complete or partial) and then progress/recur within 6 months of their last platinum dose (i.e., platinum-free interval is =\< 6 months)
* Platinum refractory ovarian cancer is defined as patients who have progression of disease while receiving platinum-based chemotherapy or who fail to achieve at least a partial response to platinum-based chemotherapy (i.e., best response to platinum-based chemotherapy is stable disease)
* Absolute neutrophil count (ANC) greater than or equal to 1,500/mcl
* Platelets greater than or equal to 100,000/mcl
* Creatinine less than or equal to 1.5 x institutional upper limit normal (ULN)
* Bilirubin less than or equal to 1.5 x ULN
* Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) less than or equal to 3 x ULN
* Alkaline phosphatase less than or equal to 2.5 x ULN
* Patients must have signed an approved informed consent and authorization permitting release of personal health information
* Patients of childbearing potential must have a negative pregnancy test prior to the study entry and be practicing an effective form of contraception

Exclusion Criteria:

* Patients who have had previous treatment with veliparib (ABT-888) or any other poly (adenosine diphosphate \[ADP\]-ribose) polymerase 1 (PARP) inhibitor (including olaparib); note: Iniparib (BSI-201) cannot inhibit PARP1 at pharmacologically achievable concentrations, therefore prior iniparib therapy is allowed
* Patients with a history of other invasive malignancies, with the exception of non-melanoma skin cancer and other specific malignancies, are excluded if there is any evidence of other malignancy being present within the last three years; patients are also excluded if their previous cancer treatment contraindicates this protocol therapy
* Patients who have received prior radiotherapy to any portion of the abdominal cavity or pelvis OTHER THAN for the treatment of ovarian, fallopian tube, or primary peritoneal cancer within the last three years are excluded; prior radiation for localized cancer of the breast, head and neck, or skin is permitted, provided that it was completed more than three years prior to registration, and the patient remains free of recurrent or metastatic disease
* Patients who have received prior chemotherapy for any abdominal or pelvic tumor OTHER THAN for the treatment of ovarian, fallopian tube, or primary peritoneal cancer within the last three years are excluded; patients may have received prior adjuvant chemotherapy for localized breast cancer, provided that it was completed more than three years prior to registration, and that the patient remains free of recurrent or metastatic disease
* Patients with seizures or history or seizures are ineligible
* Patients with history or evidence upon physical examination of central nervous system (CNS) disease, including primary brain tumor, any CNS metastases, or history of cerebrovascular accident (CVA, stroke), transient ischemic attack (TIA) or subarachnoid hemorrhage within six months of the first date of treatment on this study are ineligible; patients with CNS metastases must be stable for \> 3 months after treatment and off steroid treatment prior to study enrollment
* Inability or unwillingness to swallow pills
* Patients with clinical symptoms or signs of gastrointestinal obstruction and/or who require parenteral hydration or nutrition
* Patients who are pregnant or nursing