Inclusion Criteria:

- Have a diagnosis of hormone receptor positive (HR+), human epidermal growth factor receptor 2 negative (HER2-) breast cancer. - To fulfill the requirement of HR+ disease, a breast cancer must express, by immunohistochemistry, at least 1 of the hormone receptors (estrogen receptor or progesterone receptor). - To fulfill the requirement of HER2- disease, a breast cancer must not demonstrate, at initial diagnosis or upon subsequent biopsy, overexpression of HER2 by either immunohistochemistry or in-situ hybridization.

- Have recurrent, locally advanced, unresectable or metastatic breast cancer with disease progression following anti-estrogen therapy.

- Have a performance status of 0 to 2 on the Eastern Cooperative Oncology Group scale.

- Have discontinued all previous therapies for cancer (including chemotherapy, radiotherapy, immunotherapy, and endocrine therapy) for at least 21 days for myelosuppressive agents or 14 days for nonmyelosuppressive agents prior to receiving abemaciclib, and recovered from the acute effects of therapy (until the toxicity resolves to either baseline or at least Grade 1) except for residual alopecia and peripheral neuropathy.

- Have adequate organ function, including: - Hematologic: absolute neutrophil count ≥1.5 × 10⁹/Liter (L), platelets ≥100 × 10⁹/L, and hemoglobin ≥8 grams/deciliter. Participants may receive erythrocyte transfusions to achieve this hemoglobin level at the discretion of the treating physician. Initial treatment should not begin earlier than the day after the erythrocyte transfusion. - Hepatic: bilirubin ≤1.5 × the upper limit of normal (ULN) and alanine aminotransferase ≤3 × ULN. - Renal: serum creatinine ≤ULN.

- If a woman of child-bearing potential, must test negative for pregnancy at the time of enrollment based on serum pregnancy test, and must agree to use a reliable method of birth control during the program and for 3 months following the last dose of the abemaciclib.

- If a man, must agree to use a reliable method of birth control and to not donate sperm during the program and for at least 3 months following the last dose of abemaciclib (or country requirements, whichever is longer).

- Are able to swallow capsules.

Exclusion Criteria:

- Are currently enrolled in a clinical trial involving an investigational product or concurrently enrolled in any other type of medical research judged not to be scientifically or medically compatible with this program.

- Have progressive central nervous system metastasis that require immediate local therapy including (but not limited to) whole-brain radiotherapy, stereotactic radiosurgery, surgical resection, or intrathecal chemotherapy.

- Have a history of progressive disease during prior therapy with a cyclin-dependent kinase (CDK) 4&6 inhibitor.

- Have had major surgery within 14 days of the initial dose of abemaciclib.

- Have a personal history of any of the following conditions: syncope of either unexplained or cardiovascular etiology, ventricular tachycardia, ventricular fibrillation, or sudden cardiac arrest.

- Have active bacterial, fungal, and/or known viral infection.

- If lactating, must agree to not begin and/or discontinue breastfeeding.