Evaluate the Safety, Immunologic, and Virologic Responses of Donor Derived (DD) HIV-Specific T-cells (HST) in HIV-infected Individuals Following Allogeneic Bone Marrow Transplantation (alloRESIST)

Inclusion Criteria: Participant Inclusion Criteria at Screening: * Age ≥18 years. * Confirmation of HIV-1 infection. Any licensed ELISA test kit which is confirmed by Western blot or Multispot HIV-1/HIV-2 assay prior to screening. HIV culture, HIV antigen, plasma HIV RNA, or a second antibody test by a method other than ELISA is acceptable as an alternative confirmatory test. * On effective antiretroviral therapy. * Ability and willingness of participant to continue and be compliant with ART throughout the study. * Hematologic malignancy that qualifies for standard of care alloBMT according to JHU criteria. * Potential participant must have adequate organ function for standard of care alloBMT according to JHU criteria. * No active HCV infection. (If seropositive, participant must have no measureable HCV RNA within 30 days of enrollment). * No active HBV infection (If seropositive, participant must have no measureable HBV DNA or HBsAg+ within 30 days of enrollment). * Ability and willingness of participant to give written informed consent. * Ability and willingness to communicate effectively with study personnel; considered reliable, willing, and cooperative in terms of compliance with the Protocol requirements. * Ability and willingness to provide adequate locator information and contact information for at least 2 adults who can reach the participant within 24 hours Participant Inclusion Criteria for DD HST-NEETs Infusion: * Karnofsky score of ≥ 70. * ANC ≥ 250/µL. * Bili…