Cord Blood Transplant With Dilanubicel for the Treatment of HIV Positive Hematologic Cancers

This phase II trial studies the side effects of a cord blood transplant using dilanubicel and to see how well it works in treating patients with human immunodeficiency virus (HIV) positive hematologic (blood) cancers. After a cord blood transplant, the immune cells, including white blood cells, can take a while to recover, putting the patient at increased risk of infection. Dilanubicel consists of blood stem cells that help to produce mature blood cells, including immune cells. Drugs used in chemotherapy, such as fludarabine, cyclophosphamide, and thiotepa, 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. Total body irradiation is a type of whole-body radiation. Giving chemotherapy and total-body irradiation before a cord blood transplant with dilanubicel may help to kill any cancer cells that are in the body and make room in the patient's bone marrow for new stem cells to grow and reduce the risk of infection.

OUTLINE: Patients are assigned to 1 of 2 regimens.

REGIMEN A: Patients receive fludarabine intravenously (IV) over 30 minutes on days -8 to -6, cyclophosphamide IV on days -7 to -6, and undergo total body irradiation (TBI) twice daily (BID) on days -4 to -1. Patients then undergo umbilical cord blood transplant on day 0. Between 4-24 hours after transplant completion, patients receive dilanubicel IV over 5-10 minutes in the absence of disease progression or unacceptable toxicity.

REGIMEN B: Patients receive fludarabine IV over 30-60 minutes on days -6 to -2, cyclophosphamide IV on day -6, thiotepa IV over 4 hours on days -5 to -4, and undergo TBI once daily (QD) on days -2 to -1. Patients then undergo umbilical cord blood transplant on day 0. Between 4-24 hours after transplant completion, patients receive dilanubicel IV over 5-10 minutes in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up at 28, 80, and 180 days, and then at 1 and 2 years.

Eligibility Criteria:
Inclusion Criteria:

* \>= 6 months to =\< 65 years
* Treatment with combination antiretroviral therapy (cART) for at least 1 month before enrollment
* Viral load \< 5000 copies/ml plasma on cART
* Disease criteria

  * Acute myeloid leukemia

    * High risk in first complete remission (CR1), \>= 2 cycles to obtain complete remission (CR), erythroblastic or megakaryocytic leukemia; \>= in second complete remission (CR2)
    * All patients must be in CR as defined by hematologic recovery and \< 5% blasts by morphology within the bone marrow and a cellularity of \>= 15%
    * Patients for whom adequate marrow/biopsy specimens cannot be obtained to determine remission status by morphologic assessment, but have fulfilled criteria of remission by flow cytometry, recovery of peripheral blood counts with no circulating blasts, and/or normal cytogenetics (if applicable) may still be eligible. Specimen for morphologic assessment, including possible repeat procedures will be obtained (as possible). These patients must be discussed with the lead principal investigator, Filippo Milano prior to enrollment
  * Acute lymphoblastic leukemia

    * High risk CR1 (for example, but not limited to: t(9;22), t(1;19), t(4;11) or other mixed-lineage leukemia \[MLL\] rearrangements, hypodiploid); greater than 1 cycle to obtain CR; \>= CR2
    * All patients must be in CR as defined by hematologic recovery and \< 5% blasts by morphology within the bone marrow and a cellularity of \>= 15%
    * Patients in which adequate marrow/biopsy specimens cannot be obtained to determine remission status by morphologic assessment, but have fulfilled criteria of remission by flow cytometry, recovery of peripheral blood counts with no circulating blasts, and/or normal cytogenetics (if applicable) may still be eligible. Specimen for morphologic assessment, including possible repeat procedures will be obtained (as possible). These patients must be discussed with the lead principal investigator, Filippo Milano prior to enrollment
  * Chronic myelogenous leukemia excluding refractory blast crisis. To be eligible in first chronic phase (CP1) patient must have failed or be intolerant to imatinib mesylate
  * Myelodysplasia (MDS) International Prognostic Scoring System (IPSS) intermediate (Int)-2 or high risk (i.e., refractory anemia with excess blasts \[RAEB\], refractory anemia with excess blasts in transformation \[RAEBt\]) or refractory anemia with severe pancytopenia or high-risk cytogenetics. Blasts must be \< 10% by a representative bone marrow aspirate morphology
  * Other hematologic malignancy such as non-Hodgkin lymphomas. Fred Hutch site: These patients must be presented at Patient Care Conference (PCC) prior to enrollment, given potential competing eligibility on auto-transplant protocols. Participating centers: These patients must be discussed with the lead principal investigator, Filippo Milano prior to enrollment
* Karnofsky (\>= 16 years old) \>= 70%
* Lansky (\< 16 years old) \>= 50%
* Adults: Calculated creatinine clearance must be \> 60 mL and serum creatinine =\< 2 mg/dL
* Children (\< 18 years old): Calculated creatinine clearance must be \> 60 mL/min
* Total serum bilirubin must be \< 3 mg/dL
* Transaminases must be \< 3 x the upper limit of normal
* Diffusion capacity of the lung for carbon monoxide (DLCO) corrected \> 50% normal or for pediatric patients in whom DLCO cannot be measured has adequate pulmonary function
* Left ventricular ejection fraction \> 45% OR
* Shortening fraction \> 26%
* Ability to understand and the willingness to sign a written informed consent document (adult subject or parent/legal guardian of minor subject)

Exclusion Criteria:

* Uncontrolled viral or bacterial infection at the time of study enrollment
* Active or recent (prior 6 month) invasive fungal infection without infectious disease (ID) consult and approval
* Pregnant or breastfeeding
* Prior myeloablative transplant within the last 6 months
* Extensive prior therapy including \> 12 months alkylator therapy or \> 6 months alkylator therapy with extensive radiation
* Central nervous system (CNS) leukemic involvement not clearing with intrathecal chemotherapy. Diagnostic lumbar puncture to be performed