Paclitaxel, Cisplatin, and Veliparib in Treating Patients With Advanced, Persistent, or Recurrent Cervical Cancer

Inclusion Criteria: * Patients must have primary stage IVB, recurrent or persistent squamous cell carcinoma, adenosquamous carcinoma, or adenocarcinoma of the cervix which is not amenable to curative treatment with surgery and/or radiation therapy; histologic documentation of the original primary tumor is required via the pathology report * All patients in the phase II portion must have measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1; measureable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest dimension 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; measurable disease is not required for participation in the phase I portion of this study * Patients in the phase II portion must have at least one ?target lesion? to be used to assess response on this protocol as defined by RECIST 1.1; 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 must have a Gynecologic Oncology Group (GOG) Performance Status of 0, 1, or 2 * Recovery from effects of recent surgery, radiotherapy or other therapy * 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 * At least six weeks must have elapsed from the last administration of chemoradiotherapy, and at least three weeks must have elapsed from the last administration of radiation therapy alone; at least six weeks must have elapsed from the time of any major surgical procedure prior to randomization * Absolute neutrophil count (ANC) greater than or equal to 1,500/mcl * Platelets greater than or equal to100,000/mcl * Hemoglobin \>= 9 gm/dL * Creatinine less than or equal to institutional upper limit normal (ULN) or calculated creatinine clearance (Cockcroft-Gault) \>= 60 ml/min * Calcium, magnesium, phosphate, and potassium levels within institutional normal limits * 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 * Neuropathy (sensory and motor) less than or equal to grade 1 * 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; women of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * PHASE I: All patients must have received prior chemoradiation * PHASE I: Patients do not need to have measurable disease Exclusion Criteria: * Patients with prior treatment with ABT-888 or other poly adenosine phosphate (ADP) ribose polymerase (PARP) inhibitors * 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 the 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 cervical 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 cervical 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 previously treated with chemotherapy for cervical cancer except when used concurrently with radiation therapy and/or as adjuvant therapy * Chemotherapy administered concurrent with primary radiation (e.g., weekly cisplatin) is allowed; adjuvant chemotherapy given following the completion of radiation therapy (or concurrent chemotherapy and radiation therapy) is allowed (e.g., paclitaxel and carboplatin for up to 4 cycles) * Patients may not be receiving any other investigational agents * Patients with a history of allergic reactions attributed to compounds of similar chemical or biologic composition to ABT-888 or other agents used in study * Patients with uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with ABT-888 * Patients with history or evidence upon physical examination of central nervous system (CNS) disease, including primary brain tumor, any brain metastases, or history of cerebrovascular accident (CVA, stroke), transient ischemic attack (TIA) or subarachnoid hemorrhage within 6 months of the first date of treatment on this study * Patients who are unable to swallow medication * Patients who are breast feeding should be excluded