Chimeric Antigen Receptor (CAR) T Cells With a Chlorotoxin Tumor-Targeting Domain for the Treatment of MMP2+ Recurrent or Progressive Glioblastoma

This phase I trial studies the side effects and best dose of chimeric antigen receptor (CAR) T cells with a chlorotoxin tumor-targeting domain in treating patients with MPP2+ glioblastoma that has come back (recurrent) or that is growing, spreading, or getting worse (progressive). Vaccines made from a gene-modified virus may help the body build an effective immune response to kill tumor cells.

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative. Assent, when appropriate, will be obtained per institutional guidelines. 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 main consent is processed. However, the research participant is allowed to proceed with surgery/rickham placement and CAR T cell infusion only after the translated main consent form is signed. * Agreement to allow the use of archival tissue from diagnostic tumor biopsies. If unavailable, exceptions may be granted with study principal investigator (PI) approval * Karnofsky performance status (KPS) \>= 60% * Eastern Cooperative Oncology Group (ECOG) =\< 2 * Life expectancy \>= 4 weeks * Participant has a prior histologically-confirmed diagnosis of a grade IV glioblastoma, or has a prior histologically-confirmed diagnosis of a grade II or III malignant brain tumors and now has radiographic progression consistent with a grade IV glioblastoma * Relapsed disease: radiographic evidence of recurrence/progression of measurable disease after standard therapy, and \>= 12 weeks after completion of front-line radiation therapy * City of Hope (COH) Clinical Pathology confirms matrix metalloproteinase (MMP)2+ tumor expression by immunohistochemistry (\>= 20% moderate/high MMP2 \[2+/3+\]) * No known contraindications to leukapheresis, steroids, or tocilizumab * White blood cell (WBC) \> 2000 /dl (or absolute neutrophil count \[ANC\] \>= 1,000/mm\^3) (to be performed within 14 days prior to leukapheresis unless otherwise stated) * Platelets \>= 75,000/mm\^3 (to be performed within 14 days prior to leukapheresis unless otherwise stated) * Hemoglobin \>= 8 g/dl (to be performed within 14 days prior to leukapheresis unless otherwise stated) * Total bilirubin =\< 1.5 upper limit of normal (ULN) (to be performed within 14 days prior to leukapheresis unless otherwise stated) * Aspartate aminotransferase (AST) =\< 2.5 x ULN (to be performed within 14 days prior to leukapheresis unless otherwise stated) * Alanine aminotransferase (ALT) =\< 2.5 x ULN (to be performed within 14 days prior to leukapheresis unless otherwise stated) * Serum creatinine =\< 1.6 mg/dL (to be performed within 14 days prior to leukapheresis unless otherwise stated) * Oxygen (O2) saturation \>= 95% on room air (to be performed within 14 days prior to leukapheresis unless otherwise stated) * Seronegative for human immunodeficiency virus (HIV) antigen (Ag)/antibody (Ab) combo (to be performed within 14 days prior to leukapheresis unless otherwise stated) * Women of childbearing potential (WOCBP): negative urine or serum pregnancy test (to be performed within 14 days prior to leukapheresis unless otherwise stated) * If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * 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 3 months after the last dose of CAR T cells * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) Exclusion Criteria: * Prior and concomitant therapies * Owing to higher frequency of wound-related complications, participants who are within 3 months of having received prior bevacizumab therapy at the time of enrollment are excluded. * Participant has not yet recovered from toxicities of prior therapy * Other illnesses or conditions * Uncontrolled seizure activity and/or clinically evident progressive encephalopathy * History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agent * Active diarrhea * Clinically significant uncontrolled illness * Active infection requiring antibiotics * Known history of immunodeficiency virus (HIV) or hepatitis B or hepatitis C infection * Other active malignancy * Females only: Pregnant or breastfeeding * Any other condition that would, in the investigator's judgment, contraindicate the subject's participation in the clinical study due to safety concerns with clinical study procedures * Noncompliance * 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)