This phase II trial studies how well abemaciclib works in treating patients with ovarian or endometrial cancer that has an activation of the CDK4/6 pathway and that has come back (recurrent). Abemaciclib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Giving abemaciclib may work better for the treatment of recurrent ovarian and endometrial cancer.

PRIMARY OBJECTIVE:

I. To obtain an estimate of the proportion of patients' progression-free at 16 weeks (16 week progression free survival [PFS] rate) in patients with recurrent ovarian (including fallopian tube and primary peritoneal) or recurrent endometrial cancer following treatment with abemaciclib as a molecularly matched targeted therapy.

SECONDARY OBJECTIVE:

I. To assess objective response rate (ORR) as per Response Evaluation Criteria in Solid Tumors (RECIST), progression free survival (PFS) and safety following treatment with abemaciclib as a molecularly matched targeted therapy.

EXPLORATORY OBJECTIVES:

I. To explore the relationship between response to abemaciclib and somatic gene alterations that lead to CDK4/6 activation in ovarian cancer.

II. To explore the relationship between response to abemaciclib and hormone receptor expression levels as well as somatic gene alterations that lead to CDK4/6 activation in endometrial cancer.

OUTLINE:

Patients receive abemaciclib orally (PO) twice daily (BID) on days 1-28. Patients with tumors that are hormone receptor positive also receive anastrozole or letrozole per standard of care. Cycles repeat every 28 days in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up for 30 days, and then every 12 weeks up to 1 year.

Inclusion Criteria:

• Histologically-confirmed ovarian epithelial (including fallopian tube and primary peritoneal) cancer or endometrial cancer
• Molecular tumor board confirms that patient's archival ovarian cancer tumor specimen has been assessed using standard of care genomic profiling and demonstrates CDK4/6 activation features
• Molecular tumor board confirms that patient's archival endometrial cancer tumor specimen has been assessed using standard of care genomic profiling and is of endometrioid histology, has positive hormone receptor expression and lack of Cyclin E gene (CCNE) amplification or retinoblastoma susceptibility gene product (RB) loss
• At least one prior chemotherapy regimen for the treatment of recurrent ovarian or endometrial cancer
• Patients who received chemotherapy must have recovered (Common Terminology Criteria for Adverse Events [CTCAE] grade =< 1) from the acute effects of chemotherapy except for residual alopecia or grade 2 peripheral neuropathy prior to enrollment. A washout period of at least 21 days is required between last chemotherapy dose and study initiation
• Patients who received radiotherapy must have completed and fully recovered from the acute effects of radiotherapy. A washout period of at least 14 days is required between end of radiotherapy and study initiation
• The patient is able to swallow oral medications
• Patient has an Eastern Cooperative Oncology Group (ECOG) performance status of 0-2
• Patient must be willing and able to comply with scheduled visits, treatment plans, laboratory tests, and other study procedures
• Informed consent must be obtained in writing for all patients prior to performing study/screening procedures and prior to registration into the study
• Absolute neutrophil count (ANC) >= 1.5 x 10^9/L
• Platelets >= 100 x 10^9/L
• Hemoglobin >= 8 g/dL. 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
• Total bilirubin =< 1.5 x upper limit of normal (ULN). Patients with Gilbert's syndrome with a total bilirubin =< 2.0 times ULN and direct bilirubin within normal limits are permitted
• Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =< 3 x ULN
• Female participants of childbearing potential must have a negative serum pregnancy test within 7 days of the first dose of abemaciclib and agree to use a highly effective contraception method during the treatment period and for 3 weeks following the last dose of abemaciclib

Exclusion Criteria:

• Anticipation of immediate need for a major surgical procedure (e.g., impending bowel obstruction, gastrointestinal perforation) or radiation therapy during the trial
• Diagnosis of any second malignancy within the last 5 years, except for adequately treated basal cell or squamous cell skin cancer, or for in situ carcinoma of the cervix uteri or breast
• Treatment with chemotherapy, surgery, blood products, or an investigational agent within 3 weeks of trial enrollment
• Any of the following within 6 months prior to trial registration: myocardial infarction, severe/unstable angina pectoris, coronary/peripheral artery bypass graft, New York Heart Association (NYHA) class III or IV congestive heart failure, cerebrovascular accident or transient ischemic attack, pulmonary embolism
• Unstable brain metastases or carcinomatous meningitis
• Patient of child-bearing potential is evidently pregnant or is breast feeding. A woman with child bearing potential is defined as not surgically sterile or being post-menopausal for less than 6 months
• Patient of child-bearing potential is not willing to use adequate contraceptive precautions. Adequate effective method of contraception are those which result in low failure rates, less than 1% per year, such as non-hormonal intrauterine device (IUD), condoms, sexual abstinence or vasectomized partner
• The patient has serious preexisting medical condition(s) that would preclude participation in this study (for example, interstitial lung disease, severe dyspnea at rest or requiring oxygen therapy, history of major surgical resection involving the stomach or small bowel, or preexisting Crohn's disease or ulcerative colitis or a preexisting chronic condition resulting in baseline grade 2 or higher diarrhea)
• The patient has active bacterial infection (requiring intravenous [IV] antibiotics at time of initiating study treatment), fungal infection, or detectable viral infection (such as known human immunodeficiency virus positivity or with known active hepatitis B or C [for example, hepatitis B surface antigen positive]. Screening is not required for enrollment
• The patient has a personal history of any of the following conditions: syncope of cardiovascular etiology, ventricular arrhythmia of pathological origin (including, but not limited to, ventricular tachycardia and ventricular fibrillation), or sudden cardiac arrest
• Current use or anticipated need for: Food or drugs that are known strong CYP3A4 inhibitors (i.e. grapefruit juice, verapamil, ketoconazole, miconazole, itraconazole, posaconazole, erythromycin, clarithromycin, tilithromycin, indinavir, saquinavir, ritonavir, nelfinavir, lopinavir, atazanavir, amprenavir, fosamprenavir, nefazodone, diltiazem, and delaviridine)
• Other severe acute or chronic medical or psychiatric condition, or significant laboratory abnormality requiring further investigation that may cause undue risk for the patient's safety, inhibit protocol participation, or interfere with interpretation of trial results, and in the judgment of the investigator would make the patient inappropriate for entry into this trial