Duvelisib for Ibrutinib-Resistant Chronic Lymphocytic Leukemia/Small Lymphocytic Lymphoma

* INCLUSION CRITERIA: * Age greater than or equal to 18 years * Diagnosis of CLL or SLL as defined by the following: * CLL: clonal B cells greater than or equal to 5,000 cells/uL in the peripheral blood. * SLL: lymphadenopathy with histopathological evaluation consistent with SLL, absence of cytopenia caused by clonal marrow infiltrate, and \<5,000 B cells/uL in the peripheral blood * Immunophenotype: co-expression of CD5, CD19, CD20, and CD23. CD23 negative cases may be included if there is an absence of t(11;14). * Current treatment with ibrutinib for CLL. * Mutations in BTK and/or PLCG2 (from a Clinical Laboratory Improvement Amendments (CLIA)-certified laboratory) with measurable disease characterized by at least 1 of the following: * Lymphadenopathy: greater than or equal to 1 lymph node measuring greater than or equal to 1.5 cm in the greatest diameter * Splenomegaly: spleen measuring \> 13 cm in craniocaudal length * Lymphocytosis: greater than or equal to 5,000 B cells/ L * Bone marrow infiltration: CLL comprising greater than or equal to 30% of all cells or Progressive disease characterized by at least 1 of the following when compared with nadir values: * Lymphadenopathy: appearance of any new enlarged lymph nodes (greater than or equal to 1.5 cm) or an increase by greater than or equal to 50% in greatest determined diameter of any previous site (greater than or equal to 1.5 cm). * Splenomegaly: an increase in the cranio-caudal dimension of the spleen by greater than or equal to 2 cm from nadir, on imaging or physical exam. * Lymphocytosis: an increase in the number of blood lymphocytes by greater than or equal to 50% over nadir with greater than or equal to 5,000 cells/uL B cells not attributable to redistribution of leukemia cells from lymphoid tissues to the blood related to treatment with kinase inhibitor. * Cytopenia: occurrence of cytopenia directly attributable to CLL and unrelated to autoimmune cytopenia or treatment, as documented by a decrease of Hb levels greater than or equal to 2 g/dL or \<10 g/dL, or by a decrease of platelet counts greater than or equal to 50% or \<100,000/uL, if the marrow biopsy is consistent with the cytopenia resulting from increased marrow infiltration of clonal CLL cells. * Eastern Cooperative Oncology Group (ECOG) performance status of less than or equal to 2. * Adequate organ function as defined below Hematological: * Absolute neutrophil count (ANC) greater than or equal to 1000/uL * Platelets greater than or equal to 75,000/uL Renal: -Serum creatinine \< 2.0 mg/dL Hepatic: * Serum total bilirubin less than or equal to 1.5 X ULN except subjects with Gilbert's Syndrome * AST (SGOT) and ALT (SGPT) less than or equal to 3.0 X ULN * For women of childbearing potential (WCBP): negative serum beta human chorionic gonadotropin (beta-hCG) pregnancy test within 7 days before first treatment (WCBP defined as a sexually mature woman who has not undergone surgical sterilization or who has not been naturally postmenopausal for at least 12 consecutive months for women \>55 years of age) * Willingness of male and female subjects who are not surgically sterile or postmenopausal to use medically acceptable methods of birth control for the duration of the study treatment and 3 months after the last dose of duvelisib * Willingness and ability to participate in all required evaluations and procedures in this study protocol including swallowing capsules without difficulty * Ability to understand the purpose and risks of the study and provide signed and dated informed consent and authorization to use protected health information (in accordance with national and local subject privacy regulations) EXCLUSION CRITERIA: * Richter transformation of CLL into an aggressive lymphoma * History or concurrent condition of interstitial lung disease of any severity and/or severely impaired lung function * Prior history of drug-induced colitis or pneumonitis * Known hypersensitivity to any of the study drugs * Major surgery within 4 weeks prior to screening * Central nervous system (CNS) non-Hodgkin lymphoma (NHL); lumbar puncture not required unless CNS involvement is clinically suspected * Active cytomegalovirus (CMV) or Epstein-Barr virus (EBV) infection (i.e., subjects with detectable viral load) * Infection with hepatitis B or hepatitis C: * Subjects with a positive hepatitis B surface antigen (HBsAg)) will be excluded * Subjects with or hepatitis C antibody (HCV Ab) will be excluded, unless they have received curative treatment for hepatitis C virus (HCV) and have undetectable viral RNA by PCR. * Subjects with a positive hepatitis B core antibody (HBcAb) must have negative hepatitis B virus (HBV) deoxyribonucleic acid (DNA) to be eligible, must receive prophylaxis with entecavir (or equivalent) concomitant with duvelisib treatment, and must be periodically monitored for HBV reactivation by institutional guidelines * Investigators who strongly believe that a positive HBcAb is false due to passive immunization from previous immunoglobulin infusion therapy should consider the risk-benefit for the patient given the potential for reactivation * Infection with human immunodeficiency virus (HIV): Subjects must be receiving antiretroviral therapy, have undetectable HIV RNA viral load and CD4 cell count greater than or equal to 200/uL to be eligible, must continue antiretroviral therapy concomitant with duvelisib treatment, and must be periodically monitored for suppression of viral load and potential drug-drug interactions between antiretroviral therapy and duvelisib * Infection with human T-lymphotropic virus type 1 * History of tuberculosis treatment within the 2 years prior to randomization * History of chronic liver disease, veno-occlusive disease, alcohol abuse, or illicit drug use * Ongoing treatment with chronic immunosuppressants (e.g., cyclosporine) or systemic steroids \>20 mg of prednisone (or equivalent) once daily (QD) * Ongoing treatment for systemic bacterial, fungal, or viral infection at screening NOTE: Subjects on antimicrobial, antifungal, or antiviral prophylaxis are not specifically excluded if all other inclusion/exclusion criteria are met * Administration of a live or live attenuated vaccine within 6 weeks of randomization * Concurrent administration of medications or foods that are strong inhibitors or inducers of cytochrome P450 3A (CYP3A). No prior use within 2 weeks before the start of study intervention. * Unable to receive prophylactic treatment for pneumocystis, herpes simplex virus (HSV), or herpes zoster (VZV) at screening * Baseline left ventricular ejection fraction (LVEF) \< 45 percent * Baseline QT interval corrected with Fridericia's method (QTcF) \> 500 ms NOTE: criterion does not apply to subjects with a right or left bundle branch block (BBB) * Subjects with clinically significant medical condition of malabsorption, inflammatory bowel disease, chronic conditions which manifest with diarrhea, refractory nausea, vomiting, or any other condition that will interfere significantly with drug absorption * Female subjects who are pregnant or breastfeeding * Concurrent active malignancy that requires treatment except malignancies treated with antihormonal therapy alone, nonmelanoma skin cancer, or carcinoma in situ of the cervix. * History of stroke, unstable angina, myocardial infarction, or ventricular arrhythmia requiring medication or a pacemaker within the last 6 months prior to screening * Unstable or severe uncontrolled medical condition (e.g., unstable cardiac function, unstable pulmonary condition, uncontrolled diabetes and inflammatory GI diseases such as Crohn s Disease) or any important medical illness or abnormal laboratory finding that would, in the investigator's judgment, increase the risk to the subject associated with his or her participation in the study