Brief Summary: This pilot clinical trial studies the side effects of irradiated donor cells following stem cell transplant in controlling cancer in patients with hematologic malignancies. Transfusion of irradiated donor cells (immune cells) from relatives may cause the patient's cancer to decrease in size and may help control cancer in patients receiving a stem cell transplant.

Detailed Description: PRIMARY OBJECTIVES: I. To determine the toxicity associated with the administration of irradiated haploidentical cells (IHC) to patients with high-risk hematologic malignancies. SECONDARY OBJECTIVES: I. To determine if there is evidence of disease response associated with IHC. TERTIARY OBJECTIVES: I. To determine if treatment with the irradiated cells induces an immune response targeting tumor associated epitopes. OUTLINE: Patients are assigned to 1 of 2 cohorts. COHORT I: Within 42 days after hematopoietic engraftment (both neutrophils and platelets) after autologous hematopoietic stem cell transplantation (HSCT), patients receive initial treatment with IHC. Patients that do not have evidence of relapse or progressive disease may be treated every 8-12 weeks for up to 3 doses. COHORT II: Patients with high-risk disease receive initial treatment with IHC within 70 days after hematopoietic engraftment (both neutrophils and platelets) after allogeneic HSCT. Patients being treated for relapsed disease may receive initial treatment with IHC any time after relapse is documented. Patients that do not have evidence of relapse or progressive disease may be treated every 8-12 weeks for up to 3 doses. After completion of study treatment, patients will be followed up within 8 weeks.