Veliparib, Topotecan Hydrochloride, and Filgrastim or Pegfilgrastim in Treating Patients With Persistent or Recurrent Cervical Cancer

PRIMARY OBJECTIVES: I. To estimate the antitumor activity (objective response rate by RECIST 1.1) of ABT-888 (veliparib) 10 mg administered orally twice a day on days 1 to 5 with topotecan (topotecan hydrochloride) 0.6 mg/m\^2 administered IV once daily on days 1 to 5 of each cycle in patients with persistent or recurrent carcinoma of the cervix. II. To determine the nature and degree of toxicity of ABT-888 and topotecan in patients with persistent or recurrent carcinoma of the cervix. SECONDARY OBJECTIVES: I. To determine the duration of progression-free survival and overall survival. TERTIARY OBJECTIVES: I. To determine whether evidence of an interaction exists between study treatments and tumor expression of poly(ADP-ribos)ylation of E2 protein, E6/E7 proteins, and p53R2 in relation to progression-free and overall survival or metastasis. (Translational) II. To explore the association between methylation of FanCF and BRCA in pre-treatment tumor samples and pre- and post-treatment biopsy samples and response, progression-free and overall survival of patients, and/or metastasis. (Translational) OUTLINE: Patients receive veliparib orally (PO) twice daily and topotecan hydrochloride intravenously (IV) over 30 minutes once daily on days 1-5. Patients also receive, according to institutional standard, filgrastim subcutaneously (SC) beginning on day 6, 7, or 8 and continuing until hematopoietic recovery or pegfilgrastim SC on day 6, 7, or 8. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity. Tumor tissue samples may be collected periodically for translational studies. After completion of study treatment, patients are followed up every 3 months for 2 years and then every 6 months for 3 years.