Testing the Addition of Abemaciclib to Olaparib for Women With Recurrent Ovarian Cancer

Inclusion Criteria: * Patients must have histologically confirmed recurrent platinum-resistant epithelial ovarian carcinoma (EOC) of any histology, as defined by progression within 6 months of the last dose of platinum-based chemotherapy. Both primary platinum resistant and acquired platinum resistant patients are allowed * High-grade serous histology is required (for the dose expansion cohort only) (data on BRCA (e.g. germline BRCA, Somatic BRCA, Neither, Unknown) and homologous recombination deficiency (HRD)/Loss of Heterozygosity (LOH) (e.g. HRD \> 42/LOH \>16%, HRD score \< 42/LOH \< 16%, Unknown) is not required for study but will be collected if available * Patients must have received 1-3 prior systemic therapies * Women age \>= 18 years. Because no dosing or adverse event data are currently available on the use of abemaciclib in combination with olaparib in patients \<18 years of age, children are excluded from this study * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Hemoglobin \>= 10 g/dL (within 28 days prior to administration of study treatment) * Patients may receive erythrocyte transfusions to achieve this hemoglobin level at the discretion of the investigator. Initial treatment must not begin earlier than the day after the erythrocyte transfusion * Absolute neutrophil count \>= 1,500/mcL (within 28 days prior to administration of study treatment) * Platelets \>= 100,000/mcL (within 28 days prior to administration o…