In this phase II trial, the primary objective is to determine the progression-free survival (PFS) of the cyclin dependent kinase 4/6 inhibitor (CDK4/6i) palbociclib with fulvestrant in women and men with estrogen or progesterone receptor (ER/PR) positive, HER2-negative metastatic breast cancer (MBC) who progressed on treatment with palbociclib and an aromatase inhibitor (AI). The study will also determine the prevalence rate of estrogen receptor α (ESR1) and phosphatidylinositol-3-kinase (PI3K) mutations in the study population.