Inotuzumab Ozogamicin in Treating Patients With B-cell Acute Lymphocytic Leukemia With Positive Minimal Residual Disease

Inclusion Criteria: * Patients with B-lineage ALL in hematologic complete remission (CR) with molecular failure (ie, had never achieved an MRD-negativity status before inotuzumab ozogamicin) or had a molecular relapse (ie, 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 any level of measurable residual disease identified by multicolor flow cytometry, PCR and/or next-generation sequencing (NGS). * Patients with B-lineage ALL in at least marrow CR in salvage 1 and beyond with MRD failure at any time point after 1 month of salvage therapy are allowed, including patients who received prior allogeneic stem cell transplantation. * Patients with Ph+ ALL can be enrolled in CR1 or CR2 and beyond. A TKI will be added at the discretion of the treating physician. MRD for these patients will be defined by either 1.) a ratio of BCR-ABL1 to ABL1 by PCR of ≥ 0.01% according to the International Scale for patients with p210 transcript or a ratio of BCR-ABL1 to ABL1 by PCR of ≥ 0.01% for patients with non-p210 transcripts, or 2.) detectable MRD at any level of measurable residual disease identified by multicolor flow cytometry and/or by NGS. * Performance status of 0, 1, or 2 * Creatinine clearance \>= 15 ml/min * Bilirubin \< 1.5 X upper limit of normal (ULN) * Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) \< 3 X ULN * No active or co-existing malignancy with life expectancy less than 12 months 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 or 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