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 of study treatment) * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (within 28 days prior to administration of study treatment) * Patients with Gilbert's syndrome with a total bilirubin =\< 2.0 times ULN and direct bilirubin within normal limits are permitted * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) / alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) =\< 3 x institutional ULN, unless liver metastases are present in which case they must be =\< 5 x ULN (within 28 days prior to administration of study treatment) * Patients must have creatinine clearance estimated of \>= 51 mL/min using the Cockcroft-Gault equation or based on a 24-hour urine test (within 28 days prior to administration of study treatment) * Glomerular filtration rate (GFR) \>= 60 mL/min/1.73 m\^2 unless data exists supporting safe use at lower kidney function values, no lower than 30 mL/min/1.73 m\^2 (within 28 days prior to administration of study treatment). Estimated GFR calculated using Cockcroft-Gault equation * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated * Active hepatitis B virus (HBV) is defined by a known positive HBV surface antigen (HBsAg) result. Patients with a past or resolved HBV infection (defined as the presence of hepatitis B core antibody and absence of HBsAg) are eligible * Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load. * Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction is negative for HCV ribonucleic acid (RNA) * Patients with treated brain metastases are eligible if patient is stable for at least 4 weeks status post (s/p) radiation therapy and off corticosteroids, as ascertained by clinical examination and brain imaging (magnetic resonance imaging \[MRI\] or computed tomography \[CT\] scan) during the screening period * Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better * Postmenopausal or evidence of non-childbearing status, a negative urine or serum pregnancy test within 28 days of study treatment and confirmed prior to treatment on day 1. Postmenopausal is defined as: * Amenorrheic for 1 year or more following cessation of exogenous hormonal treatments * Luteinizing hormone (LH) and follicle stimulating hormone (FSH) levels in the postmenopausal range for women under 50 * Radiation-induced oophorectomy with last menses \> 1 year ago * Chemotherapy-induced menopause with \> 1 year interval since last menses * Surgical sterilization (bilateral oophorectomy or hysterectomy) * The effects of abemaciclib and olaparib on the developing human fetus are unknown. For this reason and because CDK-and PARP-inhibiting agents are known to be teratogenic, women of child-bearing potential and their partners, who are sexually active, must agree to the use of one highly effective form of contraception and their partner must use a male condom prior to study entry, for the duration of study participation, and for 6 months after the last dose of study treatment. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately * For the dose expansion cohort, patients must have disease amenable to biopsy for correlative studies, specifically at least 1 tumor accessible and safe for biopsy on office exam or tumor that a radiologist deems is safe for biopsy in interventional radiology department based on imaging (dose expansion cohort only). For the dose escalation cohort, patients with evaluable disease are acceptable * For inclusion in i) the optional genetic research and ii) the optional biomarker research, patients must fulfill the following criteria: * Provision of informed consent for gen