Donor Atorvastatin Treatment in Preventing Severe Acute GVHD After Nonmyeloablative Peripheral Blood Stem Cell Transplant in Patients With Hematological Malignancies

Inclusion Criteria: IF PROTOCOL 2546 SERVES AS AN ADJUNCT PROTOCOL, THE PATIENTS ONLY NEEDS TO MEET INCLUSION CRITERIA 1 THROUGH 5A * Availability of human leukocyte antigen (HLA)-identical sibling donor * Transplantation with PBSC * CSP-based postgrafting immunosuppression * Willingness to give informed consent * Patient is enrolled on an investigational nonmyeloablative HCT protocol or a nonmyeloablative treatment plan with postgrafting CSP that does not use acute GVHD as its primary endpoint (protocol 2546 serves as adjunct protocol); OR * Patient is not enrolled on an investigational nonmyeloablative HCT protocol, in which case protocol 2546 serves as an independent primary treatment protocol and the patient must meet the following inclusion and exclusion criteria: * Patients must have a hematologic malignancy treatable by nonmyeloablative HCT; the following diseases will be permitted although other diagnoses can be considered if approved by Patient Care Conference (PCC) and the principal investigator: * Aggressive non-Hodgkin lymphomas (NHL) and other histologies such as diffuse large B-cell NHL - not eligible for autologous HCT, not eligible for high-dose allogeneic HCT, or after failed autologous HCT * Mantle-cell NHL - may be treated in first complete remission (CR); (diagnostic lumbar puncture \[LP\] required pre-transplant) * Low grade NHL - with \< 6 month duration of CR between courses of conventional therapy * Chronic lymphocytic leukemia (CLL) - must have either: * Failed to meet National Cancer Institute (NCI) Working Group criteria for complete or partial response after therapy with a regimen containing fludarabine phosphate (FLU) (or another nucleoside analog) or experience disease relapse within 12 months after completing therapy with a regimen containing FLU (or another nucleoside analog) * Failed FLU-cyclophosphamide (CY)-Rituximab (FCR) combination chemotherapy at any time point; or * Have "17p deletion" cytogenetic abnormality; patients should have received induction chemotherapy but could be transplanted in 1st CR * Patients with a diagnosis of CLL (or small lymphocytic lymphoma) that progresses to prolymphocytic leukemia (PLL); or * Patients with T-cell CLL or PLL * Hodgkin lymphoma - must have received and failed frontline therapy * Multiple myeloma - must have received prior chemotherapy; consolidation of chemotherapy by autografting prior to nonmyeloablative HCT is permitted * Acute myeloid leukemia (AML) - must have \< 5% marrow blasts at the time of transplant * Acute lymphocytic leukemia (ALL) - must have \< 5% marrow blasts at the time of transplant * Chronic myeloid leukemia (CML) - Patients will be accepted if they have shown intolerance to tyrosine kinase inhibitors or are beyond first chronic phase (CP1) and if they have received previous myelosuppressive chemotherapy or HCT, and have \< 5% marrow blasts at time of transplant * Myelodysplasia (MDS)/myeloproliferative syndrome (MPS) - Patients must have \< 5% marrow blasts at time of transplant * Waldenstrom's macroglobulinemia - must have failed 2 courses of therapy * Patients \< 12 years of age must be approved by the principal investigator and by a relevant patient review committee, such as the Fred Hutchinson Cancer Research Center (FHCRC) Patient Care Conference (PCC) * Patients must have either relapsed after previous high-dose chemotherapy and autologous or allogeneic HCT, or else be ineligible for such an approach due to age, failure to mobilize sufficient hematopoietic stem cells, medical comorbidities, or patient refusal * Patients who refuse to be treated on a conventional autologous or allogeneic HCT protocol * DONOR: Age \>= 18 years * DONOR: HLA genotypically identical sibling * DONOR: Willingness to give informed consent Exclusion Criteria: IF PROTOCOL 2546 SERVES AS AN ADJUNCT PROTOCOL, THE PATIENT ONLY NEEDS TO MEET EXCLUSION CRITERIA 1 THROUGH 3 * Myeloablative preparative regimen * Participation in an investigational study that has acute GVHD as the primary endpoint * The allogeneic PBSC donor has a contraindication to statin treatment * Patients eligible for and willing to receive potentially curative high-dose chemotherapy and autologous HCT * Cardiac ejection fraction \< 30% on multi gated acquisition scan (MUGA) scan or cardiac echocardiogram (echo) or active symptomatic coronary artery disease; patients with cardiac disease should be evaluated with appropriate cardiac studies and/or cardiology consultation as clinically indicated * Corrected diffusion capacity of the lung for carbon monoxide (DLCO) \< 40% of predicted, total lung capacity (TLC) \< 30% of predicted, forced expiratory volume in one second (FEV1) \< 30% of predicted, or receiving continuous supplementary oxygen * Patients with clinical or laboratory evidence of liver disease should be evaluated in conjunction with the gastrointestinal (GI) consult service for the cause of the liver disease, its clinical severity, and the degree of portal hypertension; patients will be excluded if they are found to have fulminant liver failure, cirrhosis of the liver with evidence of portal hypertension, bridging fibrosis, alcoholic hepatitis, esophageal varices, a history of bleeding esophageal varices, hepatic encephalopathy, refractory ascites related to portal hypertension, bacterial or fungal liver abscess, chronic viral hepatitis with total serum bilirubin \> 3mg/dl, or actively symptomatic biliary disease * Patients with renal failure are eligible; however, patients with pre-existing renal insufficiency will likely have further compromise in renal function and may require dialysis * Patients who are seropositive for human immunodeficiency virus (HIV) * Women who are pregnant or breast-feeding * Fertile men or women unwilling to use contraception during HCT and for 12 months afterward * Patients with active non-hematological malignancies (except non-melanoma skin cancers) or those with non-hematological malignancies (except non-melanoma skin cancers) who have been rendered with no evidence of disease, but have a greater than 20% chance of having disease recurrence within 5 years; this exclusion does not apply to patients with non-hematologic malignancies that do not require therapy * Karnofsky score \< 60 for adult patients * Lansky-play performance score \< 50 for pediatric patients * Patients with fungal pneumonia with radiological progression after receipt of amphotericin formulation or mold-active azoles for greater than 1 month * DONOR: Age \< 18 years * DONOR: History of liver disease; a donor with a history of liver disease would be eligible if the serum alanine aminotransferase (ALT) or aspartate aminotransferase (AST) are \< 2 times upper limit of normal (ULN) * DONOR: History of myopathy * DONOR: Hypersensitivity to atorvastatin * DONOR: Pregnancy * DONOR: Nursing mother * DONOR: Current serious systemic illness * DONOR: Concurrent treatment with strong inhibitors of hepatic CYP 3A4 (i.e. clarithromycin, erythromycin, protease inhibitors, azole antifungals) * DONOR: Failure to meet local criteria for stem cell donation * DONOR: Total creatinine kinase \> 2 times the ULN