Cellular Immunotherapy Following Chemotherapy in Treating Patients With Recurrent Non-Hodgkin Lymphomas, Chronic Lymphocytic Leukemia, or B-Cell Prolymphocytic Leukemia

Inclusion Criteria: * SCREENING INCLUSION CRITERIA: * COH pathology review confirms that research participant's diagnostic material is consistent with recurrent/progressive/residual B cell lymphoproliferative neoplasms as listed below AND the research participant is not eligible for or declines COH IRB Protocol No. 13277; additionally, CD19 positivity must be documented in a pathology report if the research participant previously received CD19-targeted therapy; however, it is not a requirement that the CD19 testing be performed by a COH pathologist * Disease stratum 1 (NHL): Unclassifiable high grade lymphoma, mantle cell lymphoma, follicular lymphoma, diffuse large B-cell lymphoma (DLBCL) and all its subtypes, Burkitt lymphoma (BL), marginal zone B-cell lymphoma, hairy cell leukemia, lymphoplasmacytic lymphoma, B cell lymphoma unclassifiable with features intermediate between DLBCL and BL, B cell lymphoma unclassifiable with features intermediate between DLBCL and classical Hodgkin lymphoma, and those research participants who either declined or were not eligible for COH IRB Protocol No. 13277, or who collected autologous T cells for COH IRB Protocol No. 13277 but then became ineligible for autologous hematopoietic stem cell transplant (HSCT) or participants who have relapsed following prior T cell therapy on either COH IRB Protocol No. 09174 or 12224 may be enrolled on this study * Disease stratum 2 (CLL/PLL/SLL): chronic lymphocytic leukemia (CLL), and B-cell prolymp…