Study to Evaluate the Safety and Tolerability of Brexucabtagene Autoleucel (KTE-X19) in People With Relapsed/Refractory Chronic Lymphocytic Leukemia and Small Lymphocytic Lymphoma

Key Inclusion Criteria: * Documentation of relapsed or refractory CLL and SLL; must have received at least 2 prior lines of treatment, one of which must include a Bruton's tyrosine kinase (BTK) inhibitor. * Cohort 1 and 2: Participants with r/r CLL who have received at least 2 prior lines of treatment, one of which must include a BTK inhibitor. * Cohort 3: Participants with r/r CLL and SLL must present with ≤ 1% circulating tumor cells in peripheral blood or absolute lymphocyte count (ALC) \< 5000 cells/μL. Participants must have received at least 2 prior lines of treatment, one of which must include a BTK inhibitor. * Cohort 4: Participants with r/r CLL who have received at least 2 prior lines of treatment and must have received ibrutinib as a single agent or in comibation with anti-cluster of differentiate 20 (CD20) antibodies, B-cell lymphoma 2 (BCL-2) inhibitors, and phosphoinositide 3-kinase inhibitor (PI3k) inhibitors for at least 6 months as the last line of therapy prior to screening. Ibrutinib administration will continue up to 30 hours prior to leukapheresis. In case of treatment interruption with ibrutinib, the principal investigator should reach out to the medical monitor to discuss. * An indication for treatment per International Workshop on Chronic Lymphocytic Leukemia (IWCLL) 2018 criteria and radiographically measurable disease (at least 1 lesion \> 1.5 cm in diameter) * Adequate hematologic function as indicated by: * Platelet count ≥ 50 × 10\^9/L * Neutrophil count ≥ 0.5 × 10\^9/L * Hemoglobin ≥ 8 g/dL unless lower values are attributable to CLL * Adequate renal, hepatic, cardiac and pulmonary function defined as: * Creatinine clearance (as estimated by Cockcroft-Gault) ≥ 60 mL/min * Serum alanine aminotransferase (ALT)/aspartate aminotransferase (AST) ≤ 2.5 x upper limit of normal (ULN) * Total bilirubin ≤ 1.5 mg/dL unless participant has Gilbert's syndrome * Left ventricular ejection fraction (LVEF) ≥ 50%, no evidence of pericardial effusion, no New York Heart Association (NYHA) class III or IV functional classification, no clinically significant arrhythmias * No clinically significant pleural effusion * Baseline oxygen saturation \> 92% on room air * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * At least 2 weeks or 5 half-lives, whichever is shorter, must have elapsed since any prior systemic therapy or BTKi (ibrutinib or acalabrutinib) at the time the participant is planned for leukapheresis, except for systemic inhibitory/stimulatory immune checkpoint therapy. At least 3 half-lives must have elapsed from any prior systemic inhibitory/stimulatory immune checkpoint molecule therapy at the time the participant is planned for leukapheresis (eg, ipilimumab, nivolumab, pembrolizumab, atezolizumab, OX40 agonists, 4-1BB agonists) Key Exclusion Criteria: * A history of treatment including any of the following: * Prior cluster of differentiate 19 (CD19) directed therapy * Prior allogeneic hematopoietic stem cell transplant (SCT) or donor lymphocyte infusion (DLI) within 6 months prior to enrollment * History of autoimmune disease resulting in end-organ injury unless attributable to CLL (eg, idiopathic thrombocytopenic purpura (ITP), autoimmune hemolytic anemia (AIHA)) * Diagnosis of Richter's transformation or a history of malignancy other than non-melanoma skin cancer or carcinoma in situ (eg, skin, cervix, bladder, breast), superficial bladder cancer, asymptomatic localized low grade prostate cancer for which watch-and-wait approach is standard of care, or any other cancer that has been in remission for \> 3 years prior to enrollment * History of severe hypersensitivity reaction attributed to aminoglycosides Note: Other protocol defined Inclusion/Exclusion criteria may apply.