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)
