This trial tests a combination of low-intensity chemotherapy, ponatinib, and blinatumomab in patients with a specific type of leukemia that has returned or is not responding to treatment. Chemotherapy stops cancer cell growth, ponatinib blocks enzymes needed by cancer cells, and blinatumomab helps the immune system fight cancer. Blinatumomab is an immunotherapy that has shown significant improvement in overall survival for patients with relapsed/refractory B-cell precursor acute lymphoblastic leukemia. The goal is to see if this combination works better for these patients.