PENN-Surveillance Markers of Utility for Recurrence After (Neo)Adjuvant Therapy for Breast Cancer

Inclusion Criteria: * Histologically-confirmed primary invasive breast cancer within 5 years of study entry * Qualifying risk status, at diagnosis utilizing receptor testing by ASCO/CAP guidelines, meeting at least one of the following: * Pathologically-confirmed invasive breast cancer in axillary lymph nodes, regardless of receptors * Primary tumor with triple negative subtype: estrogen receptor (ER) \< 10%, progesterone receptor (PR) \< 10% and negative Her2-overexpression by ASCO-CAP guidelines * Primary tumor that is ER+/Her2 negative/Lymph node negative with a Breast Cancer Recurrence Score of ≥ 25 per the Genomic Health Oncotype DX breast cancer test and/or HighRisk MammaPrint * Evidence of residual disease in the breast on pathologic assessment after neoadjuvant chemotherapy * Completed all primary therapy (surgery, (neo)adjuvant chemotherapy, adjuvant radiation, and/or Her2-directed therapy) for the index malignancy at least 4 weeks prior to study entry. Concurrent receipt of adjuvant endocrine therapy and bone modifying agents is allowed per standard of care. However, tamoxifen is not allowed on recurrence prevention trials that use Hydroxychloroquine. Patients on tamoxifen may still be enrolled on Penn-Surmount as long as the treating physician is aware and tamoxifen can be stopped if patient is DTC positive. * No evidence of local or distant recurrent disease by physical examination, blood tests (CBC, LFTs, Alk Phos), or symptom-directed imaging, per NCCN guidelines. * Adequate bone marrow function as shown by: ANC \>/= 1.5x10\^9/L, Platelets \>/= 100x10\^9/L, Hb \> 9 g/dL * Adequate liver function as shown by: Serum bilirubin \</= 1.5 x ULN, ALT and AST \</= 2.5 x ULN, and INR \</= 1.5 * Normal coagulation studies: PT and PTT ≤ 1.5 x upper limit of normal per institutional laboratory range * Anti-coagulation is allowed if target INR \</= 1.5 on a stable dose of warfarin or on a stable dose of anticoagulant for \>2 weeks at time of enrollment. For patients on therapeutic anti-coagulants, medication must be clinically held peri-procedure (bone marrow aspirate) per standard clinical management. * Adequate renal function: serum creatinine \</= 1.5 x ULN * Willing to undergo bone marrow aspiration and blood specimen collection per protocol specifications * Age 18 or over and able to give informed consent Exclusion Criteria: * Concurrent enrollment on another investigational therapy * Patients receiving chronic, high dose systemic treatment with corticosteroids defined as: chronic use of cortisone \>50mg; hydrocortisone \>40mg, prednisone \>10mg, methylprednisone \>8mg or dexamethasone \>1.5mg; or another immunosuppressive agent. Topical or inhaled corticosteroids are allowed. * EKG demonstrating QTC \> 480 ms * Patients who have any severe and/or uncontrolled medical conditions or other conditions that could affect their participation in the study such as: * History or evidence of increased cardiovascular risk including any of the following: (i) current clinically significant uncontrolled arrhythmias. Exception: Subjects with controlled atrial fibrillation, (ii) History of acute coronary syndromes (including myocardial infarction and unstable angina, coronary angioplasty, or stenting within 6 months prior to enrollment, (iii) Current \>/= Class II congestive heart failure as defined by New York Heart Association * History of pneumonitis/interstitial lung disease or severely impaired lung function with a previously documented spirometry and DLCO that is 50% of the normal predicted value and/or 02 saturation that is 88% or less at rest on room air * Uncontrolled diabetes * Active (acute or chronic) or uncontrolled severe infections * Liver disease such as cirrhosis, chronic active hepatitis or chronic persistent hepatitis * A known history of HIV seropositivity as reported by the patient * History of major surgical resection involving the stomach or small bowel, or pre-existing impairment of gastrointestinal function or gastrointestinal disease (e.g., ulcerative disease, Crohn's disease, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome or small bowel resection) * Patients with an active, bleeding diathesis * History of retinopathy or retinal vein occlusion * Female patients who are pregnant or breast feeding. Women of childbearing potential must have a negative urine or serum pregnancy test. * Patients who have received prior treatment with a CDK4/6 inhibitor * Patients with a known hypersensitivity to Hydroxychloroquine or any of its derivatives * Patients with prior hydroxychloroquine exposure for a duration of \> 1 month since the completion of the patient's primary therapy (definitive surgery, (neo)adjuvant chemotherapy, adjuvant radiation, and/or Her2-directed therapy) for the index malignancy * Patients who have initiated bone modifying agents within 3 months prior to study enrollment * A detailed assessment of Hepatitis B/C medical history and risk factors must be done at screening for all patients. HBV DNA and HCV RNA PCR testing are required at screening for all patients with a positive medical history based on risk factors and/or confirmation of prior HBV/HCV infection.