Please assess the completion status of the following clinical trial:

Trial Title: A Study to Accelerate Immune System Recovery Following Stem Cell Transplantation

Study Design Characteristics:
- Allocation: NON_RANDOMIZED
- Intervention Model: SINGLE_GROUP
- Observational Model: None
- Primary Purpose: TREATMENT
- Time Perspective: None
- Masking: NONE
- Phase: PHASE2
- Number of Arms: None

Eligibility Criteria:
Inclusion Criteria:~* To be treated on this study, patients must have recently undergone a T-cell depleted allogeneic bone marrow or peripheral blood stem cell transplant from an HLA-matched sibling donor, an HLA matched unrelated donor, or an HLA partially matched (single antigen mismatched, two antigen mismatched, or haplodisparate) donor. Patients will be counseled and will sign informed consent for this study prior to their transplant. Our intention is to analyze the effectiveness of LLME treated DLI (Donor Lymphocyte Infusion) on an intent to treat basis. To proceed with this therapy after HSCT, patients must meet the other selection criteria below at the time of first DLI. Additionally, discussion prior to transplant helps present the patient (and donor) a picture of the proposed therapy in its entirety, rather than in piecemeal fashion. A patient or donor's unwillingness to participate in this study will in no way affect their eligibility for transplant therapy at our center.~* At the time of initial DLI therapy, patients must be between 28 and 42 days post allogeneic HSCT or between 28 and 42 days after the last dose of ATG if that agent was used after the transplant as part of their graft rejection prophylaxis. They must also meet the following criteria during the week prior to first infusion:~* Patients must have achieved primary engraftment with an absolute neutrophil count of at least 1000 per l for 3 consecutive days.~* Patients must have a CD4+ lymphocyte count of less than 200 per l. An absolute lymphocyte count of less than 200 per l will be taken as prime facie evidence that the CD4+ lymphocyte count meets this criteria.~* Patients may not exhibit overt hematologic manifestations of relapse or persistent disease. Evidence of recurrent/persistent disease based primarily on flow cytometry, cytogenetics, chimerism analysis, or other molecular studies does not by itself represent grounds for exclusion.~* Patients must be 16 years of age or older. There is no upper age limit for this study.~* Patients must not be pregnant.~* Patients must not have any documented graft-versus-host disease.

- Gender: ALL
- Minimum Age: 16 Years
- Maximum Age: None
- Healthy Volunteers: f

Based on this trial design, predict the completion outcome and termination type (if applicable).