This phase I trial investigates the side effects of chemotherapy and cellular immunotherapy in treating children with IL13Ralpha2 positive brain tumors that have come back after a period of improvement (recurrent) or do not respond to treatment (refractory). Cellular immunotherapy (IL13(EQ)BBzeta/CD19t+ T cells) are brain-tumor specific cells that may induce changes in body's immune system and may interfere with the ability of tumor cells to grow and spread. Chemotherapy drugs, such as as cyclophosphamide and fludarabine, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Many patients with brain tumor respond to treatment, but then the tumor starts to grow again. Giving chemotherapy in combination with cellular immunotherapy may kill more tumor cells and improve the outcome of treatment.