Blinatumomab in Treating Patients With B-cell Acute Lymphoblastic Leukemia With Minimal Residual Disease

Inclusion Criteria: * Patients with B-lineage acute lymphocytic leukemia (ALL) in hematologic complete remission (CR) with molecular failure (i.e., had never achieved an MRD-negativity status before blinatumomab) or had a molecular relapse (i.e., became MRD positive after having been MRD negative) starting at any time point after 3 months of frontline therapy; molecular disease or minimal residual disease is defined by a value of at least of 1 x 10\^-4 (0.01%) by multicolor flow cytometry and/or by next generation sequencing (NGS) * Patients with B-lineage ALL in hematologic complete remission (CR) with molecular failure (i.e., had never achieved an MRD-negativity status before blinatumomab) or had a molecular relapse (i.e., became MRD positive after having been MRD negative) starting at any time point after 3 months of frontline therapy; molecular disease or minimal residual disease is defined by a value of at least of 1 x 10-4 (0.01%) by multicolor flow cytometry and/or by next generation sequencing (NGS) * Performance status of 0, 1, or 2 * Creatinine clearance \>= 30 ml/minute * Bilirubin less than or equal to 3.0 mg/dL * No active or co-existing malignancy with life expectancy less than 12 months * Patients with Philadelphia chromosome positive (Ph+) ALL can be enrolled in CR1 or CR2 and beyond; a tyrosine kinase inhibitor (TKI) will be added at the discretion of the treating physician; MRD for these patients will be defined by PCR of 0.1% and above (International Scale) Exclusion Criteria: * Pregnant or nursing women * Known to be human immunodeficiency virus positive (HIV+) * Active and uncontrolled disease/infection as judged by the treating physician * Unable or unwilling to sign the consent form * Active central nervous system (CNS) or extramedullary disease * Monoclonal antibodies therapy within 2 weeks before study entry * Radiotherapy and cancer chemotherapy (except for intrathecal prophylaxis and/or low-dose maintenance therapy such as vinca alkaloids, mercaptopurine, methotrexate, steroids) or any investigational drug within 2 weeks before study entry