Navitoclax and Abiraterone Acetate With or Without Hydroxychloroquine in Treating Patients With Progressive Metastatic Castrate Refractory Prostate Cancer

Inclusion Criteria: * Patients must have had evidence of disease progression while receiving primary androgen suppression therapy by orchiectomy or other primary hormonal therapy and abiraterone (Specifically, patients can have received multiple prior additional androgen axis targeting agents including enzalutamide, and prior chemotherapy, but must have had progression (as defined in 5.1.2) while receiving abiraterone either currently or in the past). Patients currently on abiraterone may continue with the start of the study drug(s). * Patients must have evidence of disease progression during current or prior therapy with abiraterone with either: 1. Biochemical progression as defined as rising PSA from a nadir or baseline (whichever was lowest) confirmed on a second determination at least 1 week later that must be higher than the first and must have reached ≥2ng/ml (if no other evidence of progression); or 2. New Metastases on bone scan (at least 2); or 3. Progression of measurable disease on CT scan by RECIST criteria * Age \>18 years and an estimated life expectancy of at least 6 months. * Treatment with at least 2 months of abiraterone prior to progression * ECOG performance status ≤ 2. (See Appendix A) * Patients must be ≥ 4 weeks since completing their prior therapy (including surgery, radiation therapy or investigational therapy (including targeted small molecule agents)). All previous clinically significant treatment-related toxicities have resolved to ≤ Grade 1. Patients must be ≥ 4 weeks since prior therapy with an anti-androgen * Adequate renal function (serum creatinine ≤ 2.0 mg/dL or creatinine clearance ≥50 ml/min) * Total bilirubin must be within 1.5 X the normal institutional limits. If total bilirubin is outside the normal institutional limits, assess direct bilirubin. The direct bilirubin must be within normal parameters. Transaminases (SGOT and/or SGPT) must be less than 1.5X ULN concomitant with alkaline phosphatase less than 5X the ULN. * An ANC \>1500/μl, hemoglobin \> 8.5 g/dl, and platelet count \>100,000/mm3 are required. * Serum testosterone (total) less than 25 ng/ml at time of enrollment. * Bisphosphonates/RANK-ligand inhibitor allowed if started prior to study treatment * Patient must consent to using effective contraception while on treatment and for 3 months thereafter * Subject must voluntarily sign and date an informed consent, approved by an Independent Ethics Committee (IEC)/Institutional Review Board (IRB), prior to the initiation of any screening or study-specific procedures Exclusion Criteria: * Known infection with HIV or subject has tested positive for HIV (due to potential drug-drug interactions between anti-retroviral inhibitors and ABT-263, as well as anticipated ABT-263 mechanism based lymphopenia that may potentially increase the risk of opportunistic infections and potential drug-drug interactions with certain anti infective agents). Patients without prior HIV testing will not be required to be tested. * Second primary malignancy except most situ carcinoma (e.g. adequately treated non-melanomatous carcinoma of the skin) or other malignancy treated at least 5 years previously with no evidence of recurrence. * Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * Subject exhibits evidence of other clinically significant uncontrolled condition(s) including, but not limited to: * active systemic fungal infection; * diagnosis of fever and neutropenia within 1 week prior to study drug administration * Patients must discontinue all herbal supplements at a minimum of one week prior to initiation of therapy (such information will be collected on each patient * Requirement for routine use of hematopoietic growth factors (including granulocyte colony stimulating factor, granulocyte macrophage colony stimulating factor, or interleukin-11) or platelet transfusions to maintain absolute neutrophil counts or platelets counts above the required thresholds for study entry. * Patient has an underlying, predisposing condition of bleeding or currently exhibits signs of bleeding. The subject has a recent history of non-chemotherapy induced thrombocytopenic associated bleeding within 1 year prior to the first dose of study drug. * History or symptoms of cardiovascular disease (NYHA Class 2, 3, or 4; see Appendix B, New York Heart Association Criteria) within the last 6 months, particularly coronary artery disease, arrhythmias, or conduction defects with risk of cardiovascular instability, uncontrolled hypertension, clinically significant pericardial effusion, or congestive heart failure. * Hypersensitivity to 4-aminoquinoline compounds, including hydroxychloroquine sulfate, chloroquine phosphate and amodiaquine. * Prior history of treatment with ABT-263 * Known G-6PDH deficiency * Retinal or visual field changes from prior 4-aminoquinoline compound use such as hydroxychloroquine sulfate, chloroquine phosphate and amodiaquine. * Patients presenting with untreated cord compression are not eligible (patients with prior treatment and stability will be eligible) * Concurrent use of other investigational agent * Subject has undergone an allogeneic stem cell transplant * Subject has active peptic ulcer disease or other hemorrhagic esophagitis/gastritis * Subject has a significant history of cardiovascular disease (e.g., MI, thrombotic or thromboembolic event in the last 6 months), renal, neurologic, psychiatric, endocrinologic, metabolic, immunologic, or hepatic disease that in the opinion of the Investigator would adversely affect his/her participating in this study. Subject has received a biologic agent for anti-neoplastic intent within 30 days prior to the first dose of study drug. * Subject is currently receiving or requires anticoagulation therapy (e.g., warfarin at any dose) or any drugs (e.g., aspirin, clopidogrel, etc) or herbal supplements that affect platelet function, with the exception of low molecular weight heparin or heparin that are used to maintain the patency of a catheter. * Subject has received aspirin or warfarin within 7 days prior to the first dose of study drug. * Subject has consumed grapefruit or grapefruit products within 3 days prior to the first dose of study drug. * Received potent CYP3A inhibitors (e.g., ketoconazole) or inducers (substrates of CYP2D6) within 7 days prior to the first dose of study drug. * Subject has received rifampin within 4 days prior to first dose of ABT-263