Inotuzumab Ozogamicin and Vincristine Sulfate Liposome in Treating Patients With Relapsed or Refractory CD22+ B-cell Acute Lymphoblastic Leukemia

Inclusion Criteria: * Eastern Cooperative Oncology Group performance status between 0-2 * Serum creatinine =\< 1.5 x upper limit of normal (ULN) or calculated creatinine clearance (Cockcroft and Gault) \> 30 mL/min * Alanine aminotransferase (ALT) =\< 5 x ULN * Total bilirubin= \< 1.5 x ULN * Left ventricular ejection fraction (LVEF) \>= 40% as assessed by echocardiogram (ECHO) or multiple-gated acquisition (MUGA) scan performed within 28 days of enrollment * Diagnosis of relapsed/refractory CD22+ B-cell ALL with disease in the bone marrow and/or peripheral blood by morphology (\>=5% blasts). CD22-positive B-ALL is defined as expression by at least 20% of malignant lymphoblasts as determined by local flow cytometry and/or immunohistochemistry from a peripheral blood and/or bone marrow sample obtained within 2 weeks of screening * Relapsed or refractory disease, defined as second or greater bone marrow relapse from CR or overall response or, disease has progressed following two or more anti-leukemia therapies. Specifically: * Any bone marrow relapse after allogeneic HSCT: subjects must be at least 1 month from HSCT at the time of screening and off immunosuppressive medication for at least 2 weeks at time of initial treatment (with the exception of low-dose steroids =\< 20 mg prednisone equivalent) and have no active graft versus (vs.) host disease (GVHD); * Philadelphia chromosome (Ph) negative B-ALL which has not achieved CR or CRi after at least 2 attempts at remission…