Please assess the completion status of the following clinical trial:

Trial Title: Rituximab in Treating Patients Undergoing Donor Peripheral Blood Stem Cell Transplant for Relapsed or Refractory B-cell Lymphoma

Study Design Characteristics:
- Allocation: None
- Intervention Model: SINGLE_GROUP
- Observational Model: None
- Primary Purpose: TREATMENT
- Time Perspective: None
- Masking: NONE
- Phase: PHASE2
- Number of Arms: 1.0

Eligibility Criteria:
Inclusion Criteria:~* With a diagnosis of CD20-expressing B-cell malignancy of any histologic type or grade for whom non-myeloablative allogeneic transplant is considered an appropriate treatment option~* Who are enrolled on a non-myeloablative allogeneic HCT protocol employing total-body irradiation (TBI)-based conditioning of =\< 4.5 Gy, with or without fludarabine; this protocol may be used as an adjunct to the allogeneic arm of a tandem autologous/allogeneic transplant protocol, provided the allogeneic conditioning meets the above criteria~* Receiving unmodified peripheral blood mononuclear cell graft products~* With an appropriate related or unrelated donor; human leukocyte antigen (HLA)-haploidentical donors are excluded~* Able to give informed consent (if \>= 18 years of age), or with a legal guardian capable of giving consent (if \< 18 years of age)~Exclusion Criteria:~* Ineligible for non-myeloablative allogeneic HCT~* Receiving an HLA-haploidentical allograft~* Who are fertile but unwilling to use contraception during and for at least 12 months after HCT~* Females who are pregnant or breast-feeding

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

Study Arms:
- Treatment (rituximab pre- and post-transplant) (Type: EXPERIMENTAL): Patients receive rituximab IV, pre- and post-transplant, on days -3, 10, 24, and 38. Patients undergo donor peripheral blood stem cell transplant on day 0. Treatment continues in the absence of disease progression or unacceptable toxicity.

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