Genetically Modified Neural Stem Cells, Flucytosine, and Leucovorin for Treating Patients With Recurrent High-Grade Gliomas

Inclusion Criteria: * Patient has had a prior, histologically-confirmed, diagnosis of a grade III or IV glioma (including glioblastoma, anaplastic oligodendroglioma, or anaplastic astrocytoma, gliosarcoma, anaplastic oligodendroglioma, or anaplastic oligoastrocytoma), or has a prior, histologically-confirmed, diagnosis of a grade II glioma and now has radiographic findings consistent with a high-grade glioma (grade III or IV) * Imaging studies show evidence of recurrent, supratentorial tumor(s). The presence of infratentorial tumor is allowed as long as the patient also has supratentorial disease that is amenable to resection or biopsy. * Patient's high-grade glioma has recurred or progressed after prior treatment with brain radiation and temozolomide * Patient has a Karnofsky performance status of \>= 70% * Patient has a life expectancy of \>= 3 months * Female patients of childbearing potential and sexually-active male patients must agree to use an effective method of contraception while participating in this study; women of childbearing potential must have a negative pregnancy test =\< 2 weeks prior to registration * The patient must be in need of a craniotomy for tumor resection or a stereotactic brain biopsy for the purpose of diagnosis or differentiating between tumor progression versus treatment-induced effects following radiation therapy +/- chemotherapy * Based on the neurosurgeon's judgement, there is no anticipated physical connection between the post-resection tumor cavity and the cerebral ventricles * Absolute neutrophil count (ANC) \>= 1500 cells/mm\^3 * Platelet count \>= 100,000 cells/mm\^3 * Total bilirubin =\< 2.0 mg/dl * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) =\< 4 times the institutional upper limit of normal * Serum creatinine =\< the institutional upper limit of normal * There is no limit to the number of prior therapies * All subjects must have the ability to understand and the willingness to sign a written informed consent Exclusion Criteria: * Patient has anti-human leukocyte antigen (HLA) antibodies specific for HLA antigens expressed by the NSCs * Patient has not recovered from any toxicity of prior therapies; an interval of * At least 6 weeks must have elapsed since taking a nitrosourea-containing chemotherapy regimen * At least 4 weeks since completing a non-nitrosourea-containing cytotoxic chemotherapy regimen (except temozolomide: only an interval of 23 days is required from the last dose administered when patient has been recently treated with the standard temozolomide regimen of daily for 5 days, repeated every 28 days) * At least 2 weeks from taking the last dose of targeted agent * At least 4 weeks from the last dose of bevacizumab * Patient is unable to undergo a magnetic resonance imaging (MRI) * Patient is allergic to 5-FC, leucovorin, or 5-FU * Patient has chronic or active viral infections of the central nervous system (CNS) * Patient has a coagulopathy or bleeding disorder * Patient has an uncontrolled illness including ongoing or active infection * Patient is receiving any other investigational agents, or concurrent biological, chemotherapy, or radiation therapy * Patient has had prior therapy with neural stem cells * Patient is pregnant or breast feeding; pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is participating in this study * Patient has another active malignancy * Non-compliance; a patient has a serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the safety monitoring requirements and completion of treatment according to this protocol