ABemacicliB or Abemaciclib and HydroxYchloroquine to Target Minimal Residual Disease in Breast Cancer

Inclusion Criteria: * Histologically-confirmed, primary, invasive breast cancer diagnosed within 5 years of entry into the companion DTC screening protocol UPCC 28115 * Qualifying risk status, at diagnosis utilizing receptor testing by ASCO/CAP guidelines, meting at least one of the following: (i) Histologically positive axillary lymph nodes, regardless of receptors (ii) Primary tumor that is ER/PR/Her2 negative: estrogen receptor (ER) \< 10%, progesterone receptor (PR) \< 10% and negative for Her2-overexpression by ASCO-CAP guidelines, regardless of lymph nodes status (iii) Primary tumor that is ER+/Her2 negative/Lymph node negative with Breast Cancer Recurrence Score of \>/= 25 per the Genomic Health Oncotype DX breast cancer test and/or high risk MammaPrint (iv) Evidence of residual disease in the breast on pathologic assessment after neoadjuvant chemotherapy * Patients must have completed all primary therapy (definitive surgery, (neo)adjuvant chemotherapy adjuvant radiation and/or Her2-directed therapy) for the index malignancy at least 4 weeks prior to study entry. Prior treatment-related toxicity must be resolved or improving to Grade 1 with the exception of alopecia, Grade 2 endocrine disorders (e.g. adrenal insufficiency or thyroid disorders from prior immunotherapy) controlled on stable replacement therapy for \> 1 year, and up to Grade 3 peripheral neuropathy, prior to study enrollment. Concurrent receipt of adjuvant endocrine and bone modifying agents is allowe…