Inclusion Criteria:

* Patients must have a diagnosis of relapsed or refractory T-cell acute lymphoblastic leukemia (T-ALL) based on World Health Organization (WHO) classification. Note that patients who were diagnosed initially with lymphoblastic lymphoma but who have relapsed with T-ALL are eligible
* Patients must have evidence of acute leukemia in their peripheral blood or bone marrow. Patients must have >= 5% lymphoblasts in the peripheral blood or bone marrow within 14 days prior to registration. Patients with only extramedullary disease are not eligible
* Patients must be refractory to or have relapsed following a standard induction chemotherapy. A standard chemotherapy induction regimen is defined as any program of treatment that includes:

* Vincristine and prednisone
* Vincristine and dexamethasone
* Cytarabine and anthracycline, or
* High dose cytarabine (defined as at least 1 gr/m2 per individual dose unless adjustments were required for renal/liver function)
* Patients must have no evidence of central nervous system disease within 28 days prior to registration based on CSF studies. Patients with clinical signs or symptoms consistent with central nervous system (CNS) involvement must have a lumbar puncture which is negative for CNS involvement; the lumbar puncture must be completed within 28 days prior to registration. Note that the patients may receive intrathecal chemotherapy with the initial lumbar puncture
* Prior nelarabine therapy is not required. In addition, patients who receive nelarabine during initial induction or post-remission treatment are eligible only if the physician does not feel they would benefit from other, multi-agent chemotherapy
* Patients must be >= 18 years of age
* Patients must have a Zubrod performance status of 0-3
* Patients must have creatinine clearance > 30 mL/min within 14 days prior to registration according to the Cockcroft Gault equation
* Patients must have direct bilirubin =< 1.5 x institutional upper limit of normal (ULN) within 14 days prior to registration
* Patients must have aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 3.0 x institutional upper limit of normal (ULN) or =< 5.0 x ULN (if thought to be related to leukemic involvement) within 14 days prior to registration
* Prothrombin time (PT)/partial thromboplastin time (PTT)/fibrinogen (as clinically indicated) (within 14 days prior to registration to obtain baseline measurements)
* From comprehensive metabolic panel: sodium, potassium, chloride, carbon dioxide (CO2), and blood urea nitrogen (BUN) (within 14 days prior to registration to obtain baseline measurements)
* Patients with known human immunodeficiency virus (HIV)-infection are eligible providing they are on effective anti-retroviral therapy and have undetectable viral load at their most recent viral load test within 6 months prior to registration. (HIV viral load testing is required only for patients with known HIV infection)
* Patients with evidence of chronic hepatitis B virus (HBV) infection may be eligible provided that they have an undetectable HBV viral load within 28 days prior to registration. Patients may be currently receiving HBV treatment. (HBV viral load testing is required only for patients with known HBV infection)
* Patients with known history of hepatitis C virus (HCV) infection may be eligible provided that they have an undetectable HCV viral load within in 28 days prior to registration. Patients may be currently receiving treatment. (HCV viral load testing is required only for patients with known HCV infection)
* Patients must agree to have bone marrow and blood specimens submitted for MRD testing
* Patients must be offered the opportunity to participate in specimen banking. With patient consent, residuals from specimens submitted will be retained and banked for future research
* Patients must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines
* As a part of the Oncology Patient Enrollment Network (OPEN) registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system

Exclusion Criteria:

* Patients must not have had chemotherapy or investigational agents within 14 days prior to registration except for steroids, oral 6-mercaptopurine, oral methotrexate, vincristine, intrathecal chemotherapy, or hydroxyurea. For participants who have received radiation therapy, at least 7 days must have elapsed from the end of radiation prior to registration and participants must not currently be experiencing toxicities from radiation therapy.
* Patients must not have undergone allogeneic hematopoietic transplant within 90 days prior to registration
* Patients must have no evidence of >= grade 2 acute graft versus host disease (GVHD) or moderate or severe limited chronic GVHD and must have no history of extensive GVHD of any severity within 90 days prior to registration. Extensive GVHD is defined as 1) generalized skin involvement or 2) localized skin involvement and/or hepatic dysfunction plus liver histology or cirrhosis or involvement of eye or minor salivary organ or oral mucosa or any other target organ
* Patients must not have systemic fungal, bacterial, viral or other infection that is not controlled (defined as exhibiting ongoing signs/symptoms related to the infection and without improvement, despite appropriate antibiotics or other treatment) within 14 days prior to registration
* Patients must not be pregnant or nursing due to the teratogenic potential of the drug used on this study. Females of reproductive potential must have a negative serum pregnancy test within 14 days prior to registration. Women/men of reproductive potential must have agreed to use an effective contraceptive method during and up to 6 months after treatment. A woman is considered to be of "reproductive potential" if she has had menses at any time in the preceding 12 consecutive months. In addition to routine contraceptive methods, "effective contraception" also includes heterosexual celibacy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) defined as a hysterectomy, bilateral oophorectomy or bilateral tubal ligation. However, if at any point a previously celibate patient chooses to become heterosexually active during the time period for use of contraceptive measures outlined in the protocol, he/she is responsible for beginning contraceptive measures
* Patients must not have other active malignancies for which they have received treatments within 6 months prior to registration excluding localized malignancies that do not require systemic treatment.