CD19-Specific T Cells Post AlloSCT

Inclusion Criteria: * RECIPIENT: Patients with high risk or relapsed disease who are planning to receive, or have received prior allogeneic HSCT from an human leukocyte antigen (HLA)-matched related, or HLA-mismatched related donor; high risk is defined as patients with acute lymphoblastic leukemia who have delayed clearance of minimal residual disease, Philadelphia (Ph)-like, or complex, 11q23 or hypodiploid karyotype * RECIPIENT: Available donor who provided hematopoietic stem-cell (HSC) * RECIPIENT: Patients with CD19+ lymphoid malignancies that are refractory to or intolerant of standard treatment (as defined below): * B-cell Acute Lymphoblastic Leukemia (ALL) * Non-Hodgkin lymphoma (NHL) to include diffuse large B-cell lymphoma (DLBCL) not otherwise specified, primary mediastinal large B cell lymphoma, mantle cell lymphoma, or transformed follicular lymphoma (TFL) as defined by the World Health Organization 2008 criteria * Small lymphocytic lymphoma (SLL) * Chronic lymphocytic leukemia (CLL) * NOTE: Refractory disease for acute and chronic leukemia is defined by: * Presence of \> 5% malignant blasts in bone marrow and/or peripheral blood and/or minimal residual disease by flow cytometry or molecular analysis for fusion proteins and/or positive imaging for extra-medullary disease to most recent therapy * NOTE: Refractory disease for lymphoma is defined as: * Progressive disease or stable disease lasting =\< 6 months, as best response to most recent…