Donor Natural Killer Cells After Donor Stem Cell Transplant in Treating Patients With Advanced Cancer

DISEASE CHARACTERISTICS: * Diagnosis of a malignant disorder (hematologic malignancies or solid tumors) * Advanced disease * Has undergone prior allogeneic hematopoietic stem cell transplantation (HSCT) from an HLA-mismatched/haploidentical familial donor * Progressive or recurrent disease, as defined by any of the following (phase II): * Peripheral blood blast \> 20% with bone marrow aspirate showing \> 5% leukemic cells (in patients with acute leukemia) * Detection of metaphases in the marrow with the same clonal cytogenetic abnormalities as identified before HSCT (or by FISH markers, if appropriate) (in patients with acute leukemia or high-risk myelodysplastic syndromes \[MDS\]) * Persistent cytopenia with bone marrow aspirate showing various degrees of dysplasia involving ≥ 1 cell lineage (in patients with high-risk MDS) * Enlargement of pre-existing measurable lesions by 20% according to RECIST criteria (in patients with solid tumors or lymphoma) * Appearance of new metastatic lesions, including pleural effusion or ascites, radiologically typical for metastases or confirmed as such by cytology (in patients with solid tumors or lymphoma) * Measurable disease (phase II) PATIENT CHARACTERISTICS: * Karnofsky performance status 70-100% * Total bilirubin \< 3.0 mg/dL * AST \< 5 times upper limit of normal * Creatinine \< 3 mg/dL * Not pregnant or nursing * No clinically evident cardiac or pulmonary failure PRIOR CONCURRENT THERAPY: * See Disease Characteristics