B-Cell Activating Factor Receptor (BAFFR)-Based Chimeric Antigen Receptor T-Cells With Fludarabine and Cyclophosphamide Lymphodepletion for the Treatment of Relapsed or Refractory B-cell Hematologic Malignancies

Inclusion Criteria: * PRE-REGISTRATION: Age ≥ 18 years * PRE-REGISTRATION: Confirmed diagnosis of 1 of the following relapsed or refractory B-cell hematologic malignancies: chronic lymphocytic leukemia/small lymphocytic lymphoma (CLL/SLL), follicular lymphoma (FL), mantle cell lymphoma (MCL), marginal zone lymphoma (MZL), or large B cell lymphoma (LBCL) including Richter's transformation from CLL/SLL * For CD19+ B cell malignancies; relapsed or refractory disease is defined by one of the following histopathology: * Biopsy proven SLL or flow cytometry proven CLL; relapsed or refractory disease is defined as: * Demonstration of progressive or stable disease by positron emission tomography/computed tomography (PET/CT) or computed tomography (CT) criteria according to the international workshop on chronic lymphocytic leukemia (iwCLL) 2018 criteria * Biopsy proven B-cell non-Hodgkin lymphoma (NHL) of any histopathology (including Richter Transformation of CLL); relapsed or refractory disease is defined as: * Demonstration of progressive or stable disease by PET/CT or CT criteria as the best response to the most recent chemotherapy regimen according to the revised Lugano Response Criteria for Malignant Lymphoma * PRE-REGISTRATION: Disease Specific prior lines of therapies below: * For CLL/SLL, patients must have received ≥ two prior lines of therapy, and/or ≥ 6 months of second line prior BTK inhibition (e.g. ibrutinib or other such as acalabrutinib or zanubrutinib) and must have failed to respond to venetoclax or be intolerant. Exception: Patients in stable disease (SD) or partial response (PR) with a known ibrutinib resistance mutation (BTK or phospholipase Cγ2) may be included even if on ibrutinib therapy for less than 6 months * These patients may or may not have received prior antibody directed against cluster of differentiation 20 (CD20). * For Follicular Lymphoma, patients must have received ≥ two prior lines of therapy, including an antibody directed against CD20. * NOTE: Prior cluster of differentiation 19 (CD19) directed chimeric antigen receptor T-cell therapy (CART) must have a 100-day washout period. * For Mantle Cell Lymphoma, patients must have received ≥ two prior lines of therapy, including an antibody directed against CD20, and a BTK inhibitor. * NOTE: Prior CD19 directed CART must have a 100-day washout period. * For Marginal Zone Lymphoma, patients must have received ≥ two prior lines of therapy, including an antibody directed against CD20. * NOTE: Prior CD19 directed CART must have a 100-day washout period. * For Large B cell Lymphoma, patients must have received ≥ two prior lines of therapy, including an antibody directed against CD20. Prior exposure to CD19 directed CART will be allowed at the discretion of the Principal Investigator. * NOTE: Prior failed CD19 directed CART must have a 100-day washout period * For Richter's Transformation, patients must have received ≥two prior lines of therapy, including an antibody directed against CD20. * 100-day washout period starts from the date of the last prior CAR-T infusion. * PRE-REGISTRATION: Measurable disease * REGISTRATION: Positive BAFFR test * REGISTRATION: Measurable disease * REGISTRATION: Eastern Cooperative Oncology Group (ECOG) performance status 0, 1 or 2 * REGISTRATION: Hemoglobin ≥ 9.0 g/dL (unless due to documented marrow involvement with disease) obtained ≤14 days prior to registration * REGISTRATION: Absolute neutrophil count (ANC) ≥ 1500/mm\^3 (unless due to documented marrow involvement with disease) obtained ≤14 days prior to registration * REGISTRATION: Platelet count ≥100,000/mm\^3 (unless due to documented marrow involvement with disease) obtained ≤ 14 days prior to registration * REGISTRATION: Total bilirubin ≤ 1.5 x upper limits of normal (ULN) (Subjects with Gilbert's Syndrome may be included if their total bilirubin is ≤ 3.0 x ULN and direct bilirubin ≤ 1.5 x ULN) obtained ≤ 14 days prior to registration * REGISTRATION: Alanine aminotransferase (ALT) and aspartate transaminase (AST) ≤ 3 x ULN (≤ 5 x ULN for patients with liver involvement) obtained ≤ 14 days prior to registration * REGISTRATION: Prothrombin time (PT)/international normalized ratio (INR) /activated partial thromboplastin time (aPTT) ≤ 1.5 x ULN OR if patient is receiving anticoagulant therapy and INR or aPTT is within target range of therapy obtained ≤ 14 days prior to registration * Patients on a stable, maintenance regimen of anticoagulant therapy for ≥ 30 days prior to registration may have PT/INR measurements \> 1.5 X ULN if, in the judgment of the investigator, the patient is suitable for the study * REGISTRATION: Calculated creatinine clearance ≥45 ml/min using the Cockcroft-Gault formula obtained ≤ 14 days prior to registration * REGISTRATION: Negative pregnancy test done ≤ 7 days prior to registration, for persons of childbearing potential only. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * REGISTRATION: Provide written informed consent understand and comply with protocol-required study procedures * REGISTARTION: Patients must have an ejection fraction (EF) of ≥ 45% * REGISTRATION: Patients must have pulse ox measurements of \> 92% on room air * REGISTRATION: Willingness to provide mandatory blood specimens for correlative research * REGISTRATION: Willing to return to enrolling institution for study follow-up Exclusion Criteria: * PRE-REGISTRATION: Prior solid organ transplantation * PRE-REGISTRATION: Unstable angina, clinically significant arrhythmia, or myocardial infarction ≤ 6 months of prior to pre-registration, or grade 3 or higher pericardial effusion at the time of pre-registration * PRE-REGISTRATION: Prior anti-BAFF-R therapies * PRE-REGISTRATION: Known contraindication to lymphodepleting (LD) chemotherapy * PRE-REGISTRATION: Use of systemic antitumor therapy or investigational agent ≤ 14 days, prior to pre-registration * PRE-REGISTRATION: Receiving any other investigational agent which would be considered as a treatment for the BAFF-R * PRE-REGISTRATION: Autologous HCT ≤ 60 days prior to pre-registration * PRE-REGISTRATION: Uncontrolled intercurrent non-cardiac illness including, but not limited to: * Previous or concurrent malignancy * Ongoing or active infection * Psychiatric illness/social situations * Dyspnea at rest due to complications of advanced malignancy or other disease that requires continuous oxygen therapy \* Persons of childbearing potential who are pregnant or breastfeeding * Life Expectancy of \< 6 weeks * Persons requiring systemic corticosteroids (\>10 mg prednisone or equivalent per day) and/or other immunosuppressive therapy. Patients are allowed to use topical corticosteroids * Any other conditions that would limit compliance with study requirements * PRE-REGISTRATION: Detectable malignant cells from cerebrospinal fluid (CSF) or magnetic resonance imaging (MRI) indicating brain metastases during screening, or a history of central nervous system (CNS) involvement by malignancy (CSF or imaging) with still active disease. Note: Patients with a history of CNS involvement resolving after treatment and without active disease will be considered eligible if other inclusion criteria are met * PRE-REGISTRATION: History of a seizure disorder, major cerebrovascular ischemia/hemorrhage, dementia, cerebellar disease, or any autoimmune disease with CNS involvement * PRE-REGISTRATION: Radiation therapy ≤ 14 days prior to pre-registration * PRE-REGISTRATION: Prior allogeneic hematopoietic stem cell transplant (HCT) in ≤ 6 months prior to pre-registration; patients with active graft versus host disease (GVHD) will not be eligible regardless of duration from prior allogeneic HCT * PRE-REGISTRATION: Human immunodeficiency virus (HIV) positive patients * PRE-REGISTRATION: Subjects with New York Health Association (NYHA) class III or greater heart failure * REGISTRATION: Eligible for auto-HCT based on investigator judgement * REGISTRATION: Presence of active bacterial, viral, or fungal infection that is uncontrolled, based on investigator judgment * REGISTRATION: Patients with active hepatitis B or hepatitis C infections are excluded from the study. Patients who are documented to be HIV positive or proven HIV infection from testing are ineligible for the study. Infectious disease testing (HIV-1, HIV-2, hepatitis C virus (HCV) antibody and polymerase chain reaction (PCR), hepatitis B virus (HBV) surface antigen, HBV surface antibody, HBV core antibody) performed ≤ 45 days prior to registration may be considered for subject eligibility * REGISTRATION: Previous or concurrent malignancy, except basal cell or squamous cell skin carcinoma, adequately resected and in situ carcinoma of cervix, or a previous malignancy that was completely resected and has been in remission for ≥ 5 years prior to registration * REGISTRATION: Persons of childbearing potential who are pregnant or breastfeeding * REGISTRATION: Life expectancy of \< 6 weeks