The goal of this clinical research study is to learn if bendamustine can help to control Acute Lymphoblastic Leukemia/Lymphoma (ALL). The safety of this drug will also be studied.

Bendamustine is designed to damage and destroy the DNA of cancer cells, which may cause them to die.

Study Drug Administration:

Patient will receive bendamustine by vein over 30 minutes twice a day on Days 1-4 of every study cycle. The length of each study cycle will depend on how the disease responds to the study drug. Each cycle will last 3 to 10 weeks.

Study Visits:

Before each cycle, patient will have a physical exam, including measurement of vital signs.

One (1) time each week, blood (about 2 tablespoons) will be drawn for routine tests. These blood draws will no longer be drawn every week if at any point the disease appears to be getting better. After that, this blood will only be drawn every 2-4 weeks while patient is receiving the study drug. These blood draws can be performed by a doctor near the patient and the results will be reported to the study doctor.

On Day 21 of Cycle 1, then every 4 weeks, patient will have a bone marrow aspirate and/or biopsy to check the status of the disease. If patient's doctor thinks it is needed, bone marrow aspirates and/or biopsies may be collected more or less often, depending on the status of the disease.

Length of Treatment:

Patient may receive up to 12 cycles of the study drug. Patient will be taken off study early if the disease gets worse, if intolerable side effects occur, or if the study doctor thinks it is in patient's best interest. Patient's participation in the study will be over after they complete the follow-up visits.

Follow-up Visits:

Patient will be asked to return to the clinic every 3 to 6 months for up to 5 years after they stop receiving the study drug. Patient will be asked about any side effects or symptoms they may be having. If patient is are unable to return to MD Anderson, the follow-up visits may be conducted over the phone. Each call should last about 5 minutes.

Blood (about 2 tablespoons) will also be drawn for routine tests every 4-8 weeks during this follow-up period.

This is an investigational study. Bendamustine is FDA approved and commercially available for the treatment of chronic lymphocytic leukemia (CLL) and B-cell non-Hodgkin's lymphoma.

Up to 40 patients will take part in this study. All will be enrolled at MD Anderson.

Inclusion Criteria:

1. Patients with relapsed/ refractory lymphoid T-cell or B-cell acute lymphoblastic leukemia which has been previously treated with at least one line of chemotherapy.
2. Age >/= 18
3. Patients must have adequate organ function including adequate renal function (calculated creatinine clearance >/= 50ml/min calculated per the Cockcroft-Gault formula). Patients must have adequate hepatic function (AST or ALT < 2.5 x ULN and total bilirubin < 3X ULN) for the reference lab unless due to leukemia.
4. Patients must have adequate performance status (ECOG 0-3).
5. Female patients must not be pregnant or lactating. Female patients of childbearing potential must have a negative serum or urine pregnancy test within 2 weeks prior to study enrollment. Female patients of childbearing potential (including those <1 year postmenopausal) and male patients must agree to use contraception.
6. Patients must sign an informed consent form indicating that they are aware of the investigational nature of this study, in keeping with the policies of the hospital.
7. Patients with active CNS involvement of leukemia may be included and treated concurrently with intrathecal chemotherapy if approved by the PI.

Exclusion Criteria:

1. Patients with a known hypersensitivity (e.g., anaphylactic and anaphylactoid reactions) to bendamustine or mannitol.
2. Patients with untreated or uncontrolled life-threatening infection.
3. Patients known to be HIV positive or known to have Hepatitis B and/or C.
4. Patients must not have received chemotherapy, monoclonal antibody therapy and/or radiation therapy within 2 weeks of study enrollment unless evidence of rapid disease progression. Hydroxyurea or corticosteroids for control of blood counts is allowed.
5. Patients must not have any other medical condition, including mental illness or substance abuse, deemed by the Investigator to be likely to interfere with a patient's ability to give informed consent or cooperate and participate in the study or interfere with the interpretation of the results.