T-Cell Depletion, Donor Hematopoietic Stem Cell Transplant (HSCT), and T-Cell Infusions in Treating Patients With Hematologic Cancer or Other Diseases

DISEASE CHARACTERISTICS: * Diagnosis of any of the following hematologic cancers or other diseases: * Acute myelogenous leukemia * Relapsed or refractory disease with poor-risk cytogenetics * Acute lymphoblastic leukemia * Relapsed or refractory disease with poor-risk cytogenetics * Chronic myelogenous leukemia * Persistent disease after at least 6 months of treatment with imatinib mesylate (Gleevec) * Myelodysplasia, meeting 1 of the following criteria: * French-American-British Classification of refractory anemia with excess blasts (RAEB) or RAEB with transformation * International Prognostic Scoring System score \> 2 * Lymphoid malignancies, including non-Hodgkin lymphoma, Hodgkin disease, chronic lymphocytic leukemia, and prolymphocytic leukemia * Relapsed or refractory disease after at least 1 prior therapy * Myelofibrosis * Transfusion dependent (RBC's, platelets, or both) * Paroxysmal nocturnal hemoglobinuria (transfusion dependent) * Myeloproliferative disorder * Eosinophilic leukemia * Severe aplastic anemia * Corrected reticulocyte count \< 1% * Platelet count \< 30,000/mm³ (untransfused) * Bone marrow biopsy with \< 15% cellularity * Plasma cell leukemia * No essential thrombocytopenia or polycythemia vera * No matched related donor available * Must have an 8/8 or 7/8 serologic HLA matched unrelated donor available PATIENT CHARACTERISTICS: * Cardiac ejection fraction ≥ 45% (if \< 45%, then cardiac consult required) * Not pregnant or nursing * Negative pregnancy test * FEV\_1 and DLCO ≥ 45% predicted * Creatinine \< 2.0 mg/dL * Bilirubin \< 2.0 mg/dL * HIV negative PRIOR CONCURRENT THERAPY: * See Disease Characteristics * No prior allogeneic bone marrow transplantation * No concurrent administration of steroids with T-cell add-backs INCLUSION CRITERIA: * Patient actual weight must not be greater than 1.5x their ideal body weight * Cardiac ejection fraction \>45%. If less than 45%, a Cardiac consult will be obtained. * A suitably matched unrelated donor that is at least a 7 out of 8 HLA serologic match. * Patient is not pregnant. * FEV 1 and DLCO \> 45% predicted on pulmonary function testing. * Serum creatinine \<2.0 mg/dl, serum bilirubin \<2.0 mg/dl. * Patient and donor are HIV negative. * Diagnosis of one of the following diseases * Acute myelogenous leukemia * Relapsed disease, * Refractory disease, or * With poor-risk cytogenetics * Acute lymphoblastic leukemia * Relapsed disease, * Refractory disease, or * With poor-risk cytogenetics * Chronic myelogenous leukemia * Persistent disease after at least 6 months of treatment with Imatinib Mesylate (Gleevec) * Myelodysplasia * FAB Classification of RAEB or RAEB-T -Or- * IPSS score \>2 * Lymphoid malignancies, including non-Hodgkin's lymphoma, Hodgkin's disease, chronic lymphocytic leukemia and prolymphocytic leukemia * Relapsed or refractory disease after at least 1 prior therapy * Myelofibrosis * Transfusion dependence (RBC's, platelets, or both) * Paroxysmal Nocturnal Hemoglobinuria (PNH) * Transfusion dependent * Myeloproliferative Disorder * Eosinophilic Leukemia * Severe aplastic anemia (\<1% corrected reticulocyte count, \<30,000 untransfused platelet count, bone marrow biopsy with \<15% cellularity) * Plasma cell leukemia * Patients with ET or PV will not be candidates unless their disease has transformed to end stage myelofibrosis or acute leukemia, for which eligibility criteria for myelofibrosis or acute leukemia would apply. * Patient must signed written informed consent. EXCLUSION CRITERIA: * Inability to give informed consent * Absence of any of the above mentioned medical conditions * Availability of matched-related donor * History of prior allogeneic BMT