CAR T Cells After Lymphodepletion for the Treatment of IL13Rα2 Positive Recurrent or Refractory Brain Tumors in Children

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative. * Assent, when appropriate, will be obtained per institutional guidelines * Agreement to allow the use of archival tissue from diagnostic tumor biopsies * Karnofsky Performance Status (KPS) \>= 60% except for loss of mobility due to disease involvement; e.g., confinement to a wheelchair due to spinal cord compression * Life expectancy \> 4 weeks * Participant has a prior histologically-confirmed malignant brain neoplasm and has progressed after prior conventional therapy * Radiographic evidence of progression/recurrence of the measurable disease more than 12 weeks after the end of the initial conventional therapy (including initial radiation therapy) * City of Hope (COH) clinical pathology confirms IL13Ralpha2+ tumor expression by immunohistochemistry (IHC) at the initial tumor presentation or recurrent disease (H-score \>= 50) * If the participant has a shunt, it must be programmable and the participant must be able to tolerate the shunt being switched off for at least 2 consecutive days * Platelets \>= 50,000/mm\^3 (performed within 6 weeks of signing the main informed consent) * Total bilirubin =\< 2 X upper limit of normal (ULN) (unless has Gilbert's disease) (performed within 6 weeks of signing the main informed consent) * Aspartate transaminase (AST) =\< 2 x ULN (performed within 6 weeks of signing the main informed consent) * Alanine transferase (ALT) =\< 2 x ULN (performed within 6 weeks of signing the main informed consent) * Creatinine clearance of \>= 75mL/min/1.73m\^2 (performed within 6 weeks of signing the main informed consent) * Seronegative for human immunodeficiency virus (HIV) antigen (Ag)/antibody (Ab) combo, hepatitis C virus (HCV)\* and active HBV (surface antigen negative) (performed within 6 weeks of signing the main informed consent) * If positive, hepatitis C ribonucleic acid (RNA) quantitation must be performed * Women of childbearing potential (WOCBP): Negative urine or serum pregnancy test. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required (to be performed within 6 weeks of signing the main informed consent) * Agreement by females and males of childbearing potential\* to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 6 months after the last dose of protocol therapy. * Childbearing potential defined as not being surgically sterilized (males and females) or have not been free, once initiated, from menses for \> 1 year (females only) * ELIGIBILITY TO PROCEED WITH PERIPHERAL BLOOD MONONUCLEAR COLLECTION (PBMC) COLLECTION * Research participant must not require more than 0.1mg/kg/day total dose (0.03mg/kg/dose three times per day, max of 6mg/day) of Dexamethasone on the day of peripheral blood mononuclear cell (PBMC) collection * Research participant must have appropriate venous access * At least 2 weeks must have elapsed since the research participant received his/her last dose of prior targeted agents, chemotherapy or radiation * Note: If a research participant weighs less than 50kgs, the study team should provide the Donor Apheresis Center (DAC) with the participant's current weight so that institutional guidelines can be followed * ELIGIBILITY TO PROCEED WITH INDWELLING CENTRAL NERVOUS SYSTEM (CNS) CATHETER PLACEMENT * Serum creatinine \< 1.6 mg/dL * White blood cell (WBC) \>= 2,000/dL * Absolute neutrophil count (ANC) \>= 1,000 * Platelets \> 50,000/dL * International normalized ratio =\< 1.3 * Bilirubin \< 1.5 mg/dL * Alanine transferase (ALT) and aspartate transaminase (AST) \< 2 x upper limits of normal * KPS \>= 60% except for loss of mobility due to disease involvement; e.g., confinement to a wheelchair due to spinal cord compression * Second-line radiation therapy (post-leukapheresis) completed at least 4 weeks prior to surgical resection or biopsy/catheter placement * ELIGIBILITY TO PROCEED WITH LYMPHODEPLETION * Pulmonary: Research participant does not require supplemental oxygen to keep saturation greater than 95% and/or does not have presence of any radiographic abnormalities on chest x-ray that are progressive * Cardiac: Research participant does not require pressor support and/or does not have symptomatic cardiac arrhythmias * Active infection: Research participant does not have a fever exceeding 38.5 degree celsius; there is an absence of positive blood cultures for bacteria, fungus, or virus within 48-hours prior to CAR T cell infusion and/or there aren't any indications of meningitis * Hepatic: Research participant serum total bilirubin or transaminases does not exceed 2 x normal limit * Renal: Research participant serum creatinine \< 1.8 mg/dL * Neurologic: Research participant does not have uncontrolled seizure activity following surgery prior to starting lymphodepletion * ELIGIBILITY TO PROCEED WITH EACH CAR T CELL INFUSION * Research participant has a released cryopreserved T cell product * Research participant does not require supplemental oxygen to keep saturation greater than 95% and/or does not have presence of any radiographic abnormalities on chest x-ray that are progressive * Research participant does not require pressor support and/or does not have symptomatic cardiac arrhythmias * Research participant does not have a fever exceeding 38.5 degree celsius; there is an absence of positive blood cultures for bacteria, fungus, or virus within 48-hours prior to T cell infusion and/or there aren't any indications of meningitis * Research participant serum total bilirubin or transaminases does not exceed 2 x normal limit * Research participant serum creatinine \< 1.8 mg/dL * Research participant does not have uncontrolled seizure activity * Research participant platelet count must be \>= 50,000. However, if platelet level is between 25,000-49,000, then T-cell infusion may proceed after platelet transfusion is given and the post transfusion platelet count is \>= 50,000 * Research participants must not require more than 0.1mg/kg/day total dose (0.03mg/kg/dose three times per day, max of 6mg/day) of dexamethasone during CAR T cell therapy * Wash-out requirements: * At least 6 weeks since the completion of a nitrosourea-containing chemotherapy regimen; * At least 23 days since the completion of temozolomide and/or 4 weeks for any other non-nitrosourea-containing cytotoxic chemotherapy regimen. If a patient's most recent treatment was with a targeted agent only, and s/he has recovered from any toxicity of this targeted agent, then a waiting period of only 2 weeks is needed from the last dose * For bevacizumab the wash out period of at least 4 weeks is required before starting study treatment Exclusion Criteria: * Pulmonary: Research participant requires supplemental oxygen to keep saturation greater than 95% and the situation is not expected to resolve within 2 weeks * Cardiac: Research participant requires pressor support and/or has symptomatic cardiac arrhythmias * Renal: Research participant requires dialysis * Neurologic: Research participant has uncontrolled seizure activity and/or clinically evident progressive encephalopathy * Failure of research participant to understand the basic elements of the protocol and/or the risks/benefits of participating in this phase I study. A legal guardian may substitute for the research participant * Research participant with any non-malignant intercurrent illness which is either poorly controlled with currently available treatment, or which is of such severity that the study team deems it unwise to enter the research participant on protocol shall be ineligible * Research participant with any other active malignancies * Research participant being treated for severe infection or recovering from major surgery is ineligible until recovery is deemed complete by the study team * Research participant with any uncontrolled illness including ongoing or active infection. Research participant with known active hepatitis B or C infection; research participant with any signs or symptoms of active infection, positive blood cultures or radiological evidence of infections * Research participant who has confirmed HIV positivity within 4 weeks of enrollment * Females only: Pregnant or breastfeeding * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)