Intermittent Duvelisib Dosing in Treating Patients With Chronic Lymphocytic Leukemia or Small Lymphocytic Lymphoma

Inclusion Criteria: * Ability to understand and the willingness to sign a written informed consent document. * Histologically or flow cytometry confirmed diagnosis of B-CLL/small lymphocytic lymphoma (SLL) according to National Cancer Institute - Working Group (NCI-WG) 1996 guidelines. Patients who lack CD23 expression on their leukemia cells should be examined for (and found NOT to have) either t(11;14) or cyclin D1 overexpression, to rule out mantle cell lymphoma. * Participants have undergone \>= 1 prior chemotherapy-based or immunotherapy-based regimen or targeted therapy (e.g., inhibitors of BTK \[e.g., ibrutinib\], or BCL2 \[e.g., venetoclax\]) administered for \>= 2 cycles (\>= 8 weeks for oral therapies), and have had either documented disease progression or no response (i.e., stable disease \[SD\]) to the most recent treatment regimen. * Note: Individuals intolerant to ibrutinib therapy and those who progress on ibrutinib are eligible as long as they satisfy the above criteria. * Patients with CLL/SLL must demonstrate active disease meeting at least 1 of the International Workshop on Chronic Lymphocytic Leukemia (IWCLL) 2018 criteria for requiring treatment: * A minimum of any one of the following constitutional symptoms: * Unintentional weight loss \> 10% within the previous 6 months prior to screening. * Extreme fatigue (unable to work or perform usual activities). * Fevers of greater than 100.5 degrees Fahrenheit (F) for \>= 2 weeks without evidence of infection. * Night sweats without evidence of infection. * Evidence of progressive marrow failure as manifested by the development of, or worsening of anemia or thrombocytopenia. * Massive (i.e., \> 6 cm below the left costal margin), progressive or symptomatic splenomegaly. * Massive nodes or clusters (i.e., \> 10 cm in longest diameter) or progressive lymphadenopathy. * Progressive lymphocytosis with an increase of \> 50% over a 2-month period, or an anticipated doubling time of less than 6 months. * Autoimmune anemia or thrombocytopenia that is poorly responsive to corticosteroids. * Symptomatic or functional extranodal involvement (eg, skin, kidney, lung, spine) * Patients must have Eastern Cooperative Oncology Group (ECOG) performance status =\< 2. * Direct bilirubin =\< 2 x institutional upper limit of normal (ULN); unless due to known Gilbert's syndrome or compensated hemolysis directly attributable to CLL (prior to starting study drug). * Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) less than 2.5 x institutional ULN (prior to starting study drug). * Estimated creatinine clearance (CrCL) using the Cockcroft-Gault equation (or an alternative equation, per institutional standard) \>= 30 mL/min (prior to starting study drug). * Platelets \>= 30,000/mm\^3 independent of transfusion support, with no active bleeding, and absolute neutrophil count (ANC) \>= 500/mm\^3, unless due to disease involvement in the bone marrow (prior to starting study drug). * Participant must be able to swallow tablets or capsules. A participant with any gastrointestinal disease that would impair ability to swallow, retain, or absorb drug is not eligible. * Female participants of childbearing potential (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) must have a negative urine or serum pregnancy test within 72 hours prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. * Female participants of childbearing potential must agree to use adequate methods of contraception starting with the first dose of study therapy through 60 days after the last dose of study therapy. * Participants of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year without an alternative medical cause. * Male participants must agree to use an adequate method of contraception starting with the first dose of study therapy through 60 days after the last dose of study therapy. Exclusion Criteria: * Prior therapeutic intervention with any of the following: * Therapeutic anticancer antibodies within 4 weeks; * Radio- or toxin-immunoconjugates within 10 weeks; * Inhibitors of Bruton tyrosine kinase (BTK) (e.g., ibrutinib), BH3-mimetic venetoclax, lenalidomide and other "targeted" therapy - within 6 half-lives (i.e., 36 hours for ibrutinib) * All other chemotherapy, radiation therapy within 3 weeks prior to initiation of therapy. * PI3K inhibitors (idelalisib, copanlisib or any investigational PI3K inhibitor including duvelisib and umbralisib) at any time. * Any adverse event related to prior therapy that has not recovered to grade =\< 1. * Chronic use of corticosteroids in excess of prednisone 30 mg/day or its equivalent. * Allogeneic stem cell transplant within the past 12 months, or ongoing immunosuppressive therapy other than prednisone =\< 10 mg/day (or equivalent). * Use of strong CYP3A4 inhibitors or inducers, in the one week prior to initiating study treatment or concomitant. * Unable to receive prophylactic treatment for pneumocystis, herpes simplex virus (HSV), or herpes zoster (varicella zoster virus \[VZV\]) at screening. * History of prior malignancy except: * Malignancy treated with curative intent and no known active disease present for \>= 2 years prior to initiation of therapy on current study; * Adequately treated non-melanoma skin cancer or lentigo maligna (melanoma in situ) without evidence of disease; * Adequately treated in situ carcinomas (e.g., breast, cervical, esophageal, etc.) without evidence of disease; * Asymptomatic prostate cancer managed with "watch and wait" strategy * Uncontrolled immune hemolysis or thrombocytopenia (positive direct antiglobulin test in absence of hemolysis or history of immune-mediated cytopenias are not exclusions). * History of human immunodeficiency virus (HIV) infection or active hepatitis B or C. * History of chronic liver disease. * Major surgery (requiring general anesthesia) within 2 weeks prior to initiation of therapy. * Patients 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. * History of stroke, unstable angina, myocardial infarction, or ventricular arrhythmia requiring medication or a pacemaker within the last 6 months prior to screening. * 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). * Active uncontrolled infection. * Psychiatric illness/social situations that would limit compliance with study requirements. * Participant is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the screening visit through 120 days after the last dose of trial treatment.