PCAR-119 Bridge Immunotherapy Prior to Stem Cell Transplant in Treating Patients With CD19 Positive Leukemia and Lymphoma

Inclusion Criteria: Male and female subjects with CD19+ B cell malignancies in patients who have no available curative treatment options except stem cell transplantation, with limited prognosis (several months to \< 2 year survival) and no available treatment option to achieve complete remission prior to transplant. Some patients who have enrolled to other CD19-CAR-T cell therapy trials may be eligible if their CD19-CAR-T cells cannot be produced successfully because they have insufficient T cells to allow the CD19-CAR-T cells to be made; their T cells are inefficiently transduced with CAR viruses; or their CAR-T cell expansion is failed. All of those patients must meet the following criteria: 1. Eligible diseases: Acute lymphocytic leukemia (ALL), Chronic lymphocytic leukemia (CLL), Follicular lymphoma, Mantle cell lymphoma, B-cell prolymphocytic leukemia, and diffuse large cell lymphoma, previously identified as CD19+. 2. Patients 3 years of age or older, and must have a life expectancy \> 12 weeks. 3. Eastern cooperative oncology group (ECOG) performance status of 0-2 or karnofsky performance status (KPS) score is higher than 60. 4. Females of child-bearing potential must have a negative pregnancy test and all subjects must agree to use an effective method of contraception for up to two weeks after the last infusion of CAR NK cells. 5. Adequate bone marrow, liver and renal function as assessed by the following laboratory requirements: White blood cell count (WBC) ≥ 2500c/ml, Platelets ≥ 50×10\^9/L, Hb ≥ 9.0g/dL, lymphocyte (LY) ≥ 0.7×10\^9/L, LY% ≥ 15%, Alb ≥ 2.8g/dL, serum lipase and amylase \< 1.5×upper limit of normal, serum creatinine ≤ 2.5mg/dL, aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 5×upper limit of normal, serum total bilirubin ≤ 2.0mg/dL. These tests must be conducted within 7 days prior to registration. 6. Ability to give informed consent. Exclusion Criteria: 1. Pregnant or nursing women may not participate. 2. Active HIV, hepatitis B virus (HBV) or hepatitis C virus (HCV) infection at the time of screening. 3. Serious illness or medical condition which would not permit the patient to be managed according to the protocol, including active uncontrolled infection, major cardiovascular, coagulation disorders, respiratory or immune system, myocardial infarction, cardiac arrhythmias, obstructive/restrictive pulmonary disease, or psychiatric or emotional disorders. 4. History of severe immediate hypersensitivity to any of the agents including cyclophosphamide, fludarabine, or aldesleukin. 5. Concurrent use of systemic steroids. Recent or current use of inhaled steroids is not exclusionary. 6. The existence of unstable or active ulcers or gastrointestinal bleeding. 7. Patients need anticoagulant therapy (such as warfarin or heparin). 8. Patients need long-term antiplatelet therapy (aspirin at a dose \> 300mg/d; clopidogrel at a dose \> 75mg/d). 9. Patients using fludarabine or cladribine chemotherapy within 3 months prior to leukapheresis.