Duvelisib Maintenance for the Treatment of Peripheral T-Cell Lymphomas

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative. * Assent, when appropriate, will be obtained per institutional guidelines * Age: ≥ 18 years * Eastern Cooperative Oncology Group (ECOG) ≤ 2 * Histologically confirmed nodal T-follicular helper (TFH) cell lymphomas or PTCL-not otherwise specified (NOS). Nodal TFH cell lymphomas encompass three subtypes: * Angioimmunoblastic T-cell lymphoma (AITL)(World Health Organization 4th edition revised \[WHO4R\])/follicular helper T-cell lymphoma (TFH lymphoma), angioimmunoblastic type (International Consensus Classification \[ICC\])/nodal TFH cell lymphoma, angioimmunoblastic-type (World Health Organization 5th edition \[WHO5\]) * Nodal PTCL with TFH phenotype (nodal PTCL, TFH)(WHO4R)/TFH lymphoma, NOS (ICC)/nodal TFH cell lymphoma, NOS (WHO5) * Follicular T-cell lymphoma (FTCL)(WHO4R)/TFH lymphoma, follicular type (ICC)/ nodal TFH cell lymphoma, follicular-type (WHO5) * Completion of first-line multi-agent chemotherapy with a cyclophosphamide, doxorubicin, vincristine, prednisone (CHOP)-based regimen and documentation of complete response (CR) per Lugano criteria within the previous 6 months prior to enrollment. Prior corticosteroid monotherapy is not considered a line of therapy * Ineligible for or decline consolidative autologous stem cell transplantation. Ineligibility is defined by: * Patient deemed ineligible for high-dose chemotherapy and ASCT based on physician's assessment * AND at least one of the following criteria: * Age ≥ 65 years or * Age ≥ 18 years and Hematopoietic Cell Transplantation-specific Comorbidity Index score ≥ 3 * Recovery to ≤ grade 1 or baseline for any toxicities due to prior treatments, with the exception of peripheral neuropathy (recovery to ≤ grade 2) or alopecia * Platelets ≥ 25,000/mm\^3 * Hemoglobin ≥ 8 g/dL * CD4 lymphocyte count ≥ 50/mm\^3 (0.05 × 10\^9/L) * Total bilirubin ≤ 1.5 × upper limit of normal (ULN) (in patients with Gilbert's Syndrome a bilirubin \> 1.5 × ULN but ≤ 3 × ULN may be allowed with sponsor approval) * Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\]) ≤ 2.5 × ULN * Alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) ≤ 2.5 × ULN * Serum creatinine ≤ 2.0 × ULN or creatinine clearance ≥ 30 mL/min (estimated by Chronic Kidney Disease Epidemiology Collaboration \[CKD-EPI\] or Cockcroft-Gault equation or measured) * Seronegative for HIV antigen (Ag)/antibody (Ab) combo, hepatitis C virus (HCV), active hepatitis B virus (HBV) (surface antigen negative) OR patients with presence of hepatitis B core antibody (HBcAb), but absence of hepatitis B surface antigen (HBsAg), are eligible if hepatitis B virus (HBV) deoxyribonucleic acid (DNA) is undetectable (\< 20 IU), and if they are willing to undergo monitoring every 4 weeks for HBV reactivation. Patients positive for HCV antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA) * Women of childbearing potential (WOCBP): negative serum β-human chorionic gonadotropin (β-hCG) pregnancy test within 1 week 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. Women who are considered not to be of childbearing potential are not required to have a pregnancy test * Agreement by females and males of reproductive potential (i.e., not surgically sterile or female patients who are not postmenopausal) must be willing to use a highly effective method of contraception for the duration of study treatment and for at least 1 months after the last dose of duvelisib Exclusion Criteria: * Prior organ transplantation * Major surgery within 4 weeks prior to enrollment * Administration of a live vaccine within 30 days of cycle (C) 1 day (D) 1 * Unable to receive prophylactic treatment for pneumocystis at enrollment * Use of medications or consumption of foods that are strong inducers or inhibitors of CYP3A must be discontinued at least 2 weeks prior to study intervention. Patients who (after enrollment) require use of a strong CYP3A4 inhibitor to treat a fungal/mold infection will require dose reductions * Known central nervous system involvement by PTCL * Patients with known diagnosis of * Active cytomegalovirus (CMV) infection (patients with detectable viral load) * History of tuberculosis treatment within 2 years prior to enrollment * Known active bacterial, viral, fungal, mycobacterial, parasitic, or other infection (excluding fungal infections of nail beds) which requires systemic treatment. Patients may proceed with screening during treatment for infection, but systemic treatment must be completed by cycle 1 day 1 * If a patient has signs/symptoms suggestive of SARS-CoV-2 infection, the patient must have a negative molecular (e.g., polymerase chain reaction \[PCR\]) test or 2 negative antigen test results at least 24 hours apart. Patients who do not meet SARS-CoV-2 infection eligibility criteria must be screen-failed and may only be rescreened if the following have been met: * At least 10 days since first positive test result have passed in asymptomatic patients or at least 10 days since recovery, defined as resolution of fever without use of antipyretics and improvement in symptoms * History of cirrhosis or chronic alcohol abuse * Symptomatic inflammatory bowel disease (e.g., Crohn's disease, ulcerative colitis), celiac disease (i.e., sprue), prior gastrectomy or upper bowel removal, or any other gastrointestinal disorder or defect that would interfere with the absorption, distribution, metabolism or excretion of duvelisib * Concurrent active malignancy that could affect compliance with the protocol or interpretation of results except with permission of the principal investigator. The following are eligible without a specific waiver: nonmelanoma skin cancer, carcinoma in situ of the cervix * Evidence of significant, uncontrolled, concomitant diseases that could affect compliance with the protocol or interpretation of results, such as pulmonary disease, including obstructive pulmonary disease and history of bronchospasm, uncontrolled diabetes, severe psychiatric disorder or unstable cardiac disease as defined by one of the following: * Cardiac events such as myocardial infarction (MI), stroke or unstable angina within the past 6 months * New York Heart Association (NYHA) heart failure class III-IV * Uncontrolled atrial fibrillation or hypertension * History or presence of an abnormal electrocardiogram (ECG) that is clinically significant in the investigator's opinion, including complete left bundle branch block, second- or third-degree heart block * History of allergic reactions attributed to compounds of similar chemical or biologic composition to duvelisib * Participants who are receiving other investigational agents * Female patients who are breastfeeding * Any other condition that would, in the Investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)