Inclusion Criteria:

          -  diagnosis of HR+, HER2+ breast cancer (BC)

          -  unresectable locally advanced recurrent BC or metastatic BC

          -  adequate tumor tissue available prior to randomization

          -  measurable and/or non-measurable disease according to Response Evaluation Criteria in
             Solid Tumors (RECIST) version 1.1

          -  previously received:

               -  at least 2 HER2-directed therapies for advanced disease

               -  participant must have received trastuzumab emtansine (T-DM1) in any disease
                  setting

          -  must have received a taxane in any disease setting

          -  may have received any endocrine therapy (excluding fulvestrant)

          -  have postmenopausal status due to surgical / natural menopause or chemical ovarian
             suppression

          -  performance status (PS) of 0 to 1 on the Eastern Cooperative Oncology Group scale

          -  left ventricular ejection fraction (LVEF) of 50% or higher at baseline

          -  adequate organ function

          -  negative serum pregnancy test at baseline (within 14 days prior to randomization) and
             agree to use medically approved precautions to prevent pregnancy during the study and
             for 12 weeks following the last dose of abemaciclib if menopause induced by
             gonadotropin-releasing hormone (GnRH) agonist or radiation

          -  discontinued previous localized radiotherapy for palliative purposes or for lytic
             lesions at risk of fracture at least 2 weeks prior to randomization and recovered from
             the acute effects of therapy

          -  discontinued all previous therapies for cancer (including chemotherapy, radiotherapy,
             immunotherapy, and endocrine therapy), except trastuzumab, for at least 21 days for
             myelosuppressive agents or 14 days for nonmyelosuppressive agents prior to receiving
             study drug, and recovered from the acute effects of therapy

          -  are able to swallow capsules

        Exclusion Criteria:

          -  have visceral crisis

          -  known central nervous system (CNS) metastases that are untreated, symptomatic, or
             require steroids to control symptoms

          -  had major surgery within 14 days prior to randomization

          -  received prior treatment with any cyclin-dependent kinase (CDK) 4 and CDK 6 inhibitor

          -  received treatment with a drug that has not received regulatory approval for any
             indication within 14 or 21 days of randomization for a nonmyelosuppressive or
             myelosuppressive agent, respectively

          -  have serious preexisting medical conditions that, in the judgment of the investigator,
             would preclude participation in this study

          -  history within the last 6 months of symptomatic congestive heart failure, myocardial
             infarction, or unstable angina

          -  history within the last 12 months of any of the following conditions: syncope of
             cardiovascular etiology, ventricular tachycardia, ventricular fibrillation, or sudden
             cardiac arrest

          -  history of any other cancer (except non-melanoma skin cancer or carcinoma in-situ of
             the cervix), unless in complete remission with no therapy for a minimum of 3 years

          -  active bacterial, fungal infection, or detectable viral infection

          -  have received any recent (within 28 days prior to randomization) live virus
             vaccination

          -  hypersensitivity to trastuzumab, murine proteins, fulvestrant, or to any of the
             excipients