Cellular Immunotherapy in Treating Patients With High-Risk Acute Lymphoblastic Leukemia

Inclusion Criteria: * City of Hope (COH) pathology review confirms that research participant's diagnostic material is consistent with history of ALL with history of recurrence/progression/minimal residual disease (MRD) following prior therapy; additionally, CD19 positivity must be documented in a pathology report; however, it is not a requirement that the CD19 testing be performed by a COH pathologist; patients in second complete remission (CR2) or higher with history of CD19+ ALL on previous bone marrow biopsy are also eligible for the study * Research participants with confirmed 1st or higher relapse of disease by morphology, cytogenetics or molecular, or research participants with refractory or residual disease * Minimal residual disease (MRD) will be defined in this protocol by presence of malignant cells at 0.01% or more by flow cytometry or polymerase chain reaction (PCR) analysis at the completion of initial remission induction therapy * Participants with central nervous system (CNS) involvement by leukemia (CNS2 and CNS3) may be considered eligible after discussions with the study team. * Karnofsky performance status (KPS) of \>= 70% * Life expectancy \>= 16 weeks at time of enrollment * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control or abstinence) prior to study entry and for six months following duration of study participation; should a woman become pregnant or suspect that she is pregnant while participating on the trial, she should inform her treating physician immediately * All research participants must have the ability to understand and the willingness to sign a written informed consent * Note: For research participants who do not speak English, a short form consent may be used with a COH certified interpreter/translator to proceed with screening and leukapheresis, while the request for a translated full consent in processed; however, the research participant is allowed to proceed with lymphodepletion and T cell infusion only after the translated full consent form is signed * PROTOCOL-SPECIFIC CRITERIA: * COH pathology review confirms that research participant's diagnostic material is consistent with ALL; additionally, CD19 positivity must be documented in a pathology report; however it is not a requirement that the CD19 testing be performed by a COH pathologist * Negative serum pregnancy test for women of childbearing potential * If a research participant has undergone prior allogeneic stem cell transplant (alloSCT), and has documented =\< grade 2 graft versus host disease (GVHD) but the donor is undergoing leukapheresis, the research participant may be considered eligible for enrollment (at the discretion of the study principal investigator \[PI\]) provided that immunosuppressants can be tapered off completely prior to lymphodepletion * If the research participant is to undergo leukapheresis, he/she must have a pretreatment calculated creatinine clearance of \>= 50 mL/minute * If the research participant is to undergo leukapheresis, he/she must have a serum bilirubin =\< 2.0 mg/dl * Note: in the event a participant has elevated levels of liver enzymes possibly related to underlying disease, the participant will still be considered eligible * If the research participant is to undergo leukapheresis, he/she must have alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 times the institutional upper limits of normal * Note: in the event a patient has elevated levels of liver enzymes possibly related to underlying disease, the patient will still be considered eligible * If the research participant is to undergo leukapheresis, he/she must have ejection fraction measured by echocardiogram or multigated acquisition scan (MUGA) \> 45% (within 6 weeks of time of screening) * ELIGIBILITY TO PROCEED WITH PBMC COLLECTION * If research participant is undergoing leukapheresis he/she must have appropriate venous access * If research participant is undergoing leukapheresis, he/she must be at least 2 weeks from having received the last dose of immunosuppressant medications * Exceptions: * Steroids and tyrosine kinase inhibitors are allowed up to 7 days prior to leukapheresis * Research participant cannot be on more than 5 mg prednisone or equivalent doses of other corticosteroids at the time of leukapheresis * If research participant is undergoing leukapheresis and the research participant has undergone prior alloSCT, two months must have elapsed since allogeneic stem cell transplant to undergo PBMC collection for T cell manufacturing * If research participant is undergoing leukapheresis the last dose of prior chemotherapy, immunotherapy or radiation must be at least 2 weeks before the leukapheresis procedure * Exception rule: the wash out period for Hydrea is 48 hours * ELIGIBILITY TO UNDERGO LYMPHODEPLETION: * Please note that none of these criteria are applicable of the research participant's donor is undergoing leukapheresis * Research participant's absolute leukemic blast count does not exceed 10,000 cells/uL * Research participant has a released cryopreserved T cell product for T cell infusion on approximately day 0 * KPS \>= 70% * Non-hematological toxicity related to prior therapy must either have returned to =\< grade 3, baseline, or deemed irreversible * Participants of reproductive potential must agree to use and utilize an adequate method of contraception throughout treatment and for at least 8 weeks after T cell infusion * Not requiring supplemental oxygen or mechanical ventilation, oxygen saturation 90% or higher on room air * Not requiring pressor support, no symptomatic cardiac arrhythmias, no acute coronary syndrome, or uncontrolled hypertension * Preservation of renal function, serum creatinine did NOT increase by more than 2 fold above the normal reference range * Total bilirubin =\< 2.0 mg/dL * Note: in the event a participant has elevated levels of liver enzymes possibly related to underlying disease/disease progression, the participant will still be considered eligible * ALT and AST =\< 2.5 times the institutional upper limits of normal * Note: in the event a participant has elevated levels of liver enzymes possibly related to underlying disease/disease progression, the participant will still be considered eligible * Research participants without clinically significant encephalopathy/new focal deficits * No clinical evidence of uncontrolled active infectious process * ELIGIBILITY CRITERIA AT TIME OF INFUSION OF GENETICALLY MODIFIED T CELLS: * Please note that none of these criteria are applicable of the research participant's donor is undergoing leukapheresis * Research participant has undergone lymphodepletion * Pulmonary: not requiring supplemental oxygen or mechanical ventilation, oxygen saturation 90% or higher on room air * Cardiovascular: not requiring pressor support, no symptomatic cardiac arrhythmias, no acute coronary syndrome, or uncontrolled hypertension * Renal function: preservation of renal function, serum creatinine did NOT increase by more than 2 fold above the normal reference range * Liver function: total bilirubin =\< 2.0 mg/dL * Note: in the event a participant has elevated levels of liver enzymes possibly related to underlying disease/disease progression, the participant will still be considered eligible * Liver function: ALT and AST =\< 2.5 times the institutional upper limits of normal * Note: in the event a participant has elevated levels of liver enzymes possibly related to underlying disease/disease progression, the participant will still be considered eligible * Research participant without clinically significant encephalopathy/new focal deficits * Infectious diseases: no clinical evidence of uncontrolled active infectious process * ELIGIBILITY CRITERIA TO UNDERGO OPTIONAL T CELL ABLATION: * Please note that none of these criteria are applicable of the research participant's donor is undergoing leukapheresis * Research participant is scheduled for an alloSCT * Research participant has \>= 1% chimeric antigen receptor (CAR) modified T cells in the peripheral blood * Pulmonary criteria: not requiring supplemental oxygen or mechanical ventilation, oxygen saturation 90% or higher on room air * Cardiovascular criteria: not requiring pressor support, no symptomatic cardiac arrhythmias, no acute coronary syndrome, or uncontrolled hypertension * Renal function criteria: preservation of renal function, serum creatinine did NOT increase by more than 2 fold above the normal reference range * Liver function criteria: total bilirubin =\< 2.0 mg/dL * Note: in the event a participant has elevated levels of liver enzymes possibly related to underlying disease/disease progression, the participant will still be considered eligible * Liver function criteria: AST and ALT =\< 2.5 times the institutional upper limits of normal * Neurological: research participant without clinically significant encephalopathy/new focal deficits * Infectious diseases criteria: no clinical evidence of uncontrolled active infectious process Exclusion Criteria: * Research participants with any uncontrolled illness including ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, poorly controlled pulmonary disease or psychiatric illness/social situations that would limit compliance with study requirements * Research participants with known active hepatitis B or C infection; research participants who are human immunodeficiency virus (HIV) positive based on testing performed within 4 weeks of enrollment; research participants with any signs or symptoms of active infection, positive blood cultures or radiological evidence of infections * Research participants receiving any other investigational agents, or concurrent biological, chemotherapy, or radiation therapy * Note: Please note that the above criterion is not applicable at the time of enrollment if the research participant's donor is undergoing leukapheresis * Research participants with presence of other active malignancy; however, research participants with history of prior malignancy treated with curative intent and in complete remission are eligible * Pregnant and lactating women * Failure of research participant to understand the basic elements of the protocol and/or the risks/benefits of participating in this phase I study * History or presence of clinically relevant CNS pathology such as uncontrolled seizure disorder, recent stroke, severe brain injuries, dementia, cerebellar disease or psychosis * Any known contraindications to cyclophosphamide, fludarabine, etoposide, cetuximab or tocilizumab * Dependence on corticosteroids * Defined as doses of corticosteroids of greater than 5 mg/day of prednisone or equivalent doses of other corticosteroids * Note: topical and inhaled corticosteroids in standard doses and physiologic replacement for subjects with adrenal insufficiency are allowed * Please note that this criterion is not applicable at the time of enrollment if the research participant's donor is undergoing leukapheresis * Active autoimmune disease requiring systemic immunosuppressive therapy * Subjects, who in the opinion of the investigator, may not be able to comply with the safety monitoring requirements of the study