Patients with known human immunodeficiency virus (HIV) seropositive are not eligible Patients known to be seropositive for human immunodeficiency virus (HIV) and active hepatitis, even if liver function studies are in the eligible range Known to be seropositive for human immunodeficiency virus; Subject is known to be seropositive for, or have an active infection with, human immunodeficiency virus (HIV). Patients seropositive for the human immunodeficiency virus (HIV). Seropositive for the human immunodeficiency virus (HIV). Patients who are human immunodeficiency virus (HIV) seropositive Patients seropositive for the human immunodeficiency virus (HIV). Patients who are (human immunodeficiency virus [HIV]) seropositive Known human immunodeficiency virus (HIV) seropositive Patients who are human immunodeficiency virus (HIV) seropositive Has known human immunodeficiency virus (HIV) seropositive. Patients who are known to be seropositive for human immunodeficiency virus (HIV) Human immunodeficiency virus (HIV) seropositive, or active hepatitis A, B, or C infection Known history of human immunodeficiency virus (HIV) seropositive status Know to be seropositive for human immunodeficiency virus (HIV) Known human immunodeficiency virus (HIV) seropositive Persons who are seropositive for human immunodeficiency virus (HIV) Patients who are human immunodeficiency virus (HIV) seropositive Patient is human immunodeficiency virus seropositive. Seropositive for human immunodeficiency virus (HIV) HIV-1 seropositive Known to be human immunodeficiency virus (HIV) seropositive Patients seropositive for the human immunodeficiency virus (HIV) Known history of human immunodeficiency virus (HIV) seropositive status Known to be seropositive for human immunodeficiency virus (HIV); an HIV test is not required for entry on this protocol, but is required if the patient is perceived to be at risk Patients who are known to be human immunodeficiency virus (HIV)-seropositive Human immunodeficiency virus (HIV) seropositive; testing for HIV should be within 6 months of enrollment Seropositive for the human immunodeficiency virus Known seropositive for HIV Known to be human immunodeficiency virus (HIV) seropositive Patients seropositive for the human immunodeficiency virus (HIV). HIV-1 seropositive Seropositive for human immunodeficiency virus (HIV) HIV-1 seropositive at or before the time of lymphoma diagnosis Human immunodeficiency virus (HIV) seropositive Patients known to be seropositive for human immunodeficiency virus (HIV) and active hepatitis, even if liver function studies are in the eligible range Known seropositive for or active viral infection with human immunodeficiency virus (HIV). Known human immunodeficiency virus (HIV) seropositive. Known history of human immunodeficiency virus (HIV) seropositive status Patients who are known to be seropositive for human immunodeficiency virus (HIV) Patients seropositive for the human immunodeficiency virus (HIV) Known to be seropositive for human immunodeficiency virus (HIV) Known to be human immunodeficiency virus (HIV) seropositive Known to be human immunodeficiency virus (HIV) seropositive who are on anti-HIV drugs Known to be human immunodeficiency virus (HIV) seropositive Known seropositive for human immunodeficiency virus (HIV) Known seropositive for or active viral infection with human immunodeficiency virus (HIV) Patients who are known to be seropositive for human immunodeficiency virus (HIV) Patients known to be seropositive for human immunodeficiency virus (HIV) and/or active hepatitis, even if liver function studies are in the eligible range Known history of human immunodeficiency virus (HIV) seropositive status Human immunodeficiency virus (HIV) seropositive patients Patients who are known seropositive for human immunodeficiency virus (HIV) Seropositive for the human immunodeficiency virus (HIV) Known or suspected human immunodeficiency virus (HIV) infection or patients who are HIV seropositive; Human immunodeficiency virus (HIV) seropositive Patients who are known seropositive for or who have active viral infection with human immunodeficiency virus (HIV) are not eligible Known history of a human immunodeficiency virus (HIV) seropositive test Known to be human immunodeficiency virus (HIV) seropositive Known human immunodeficiency virus (HIV)-seropositive and are taking anti-retrovirals may not participate in this study; participants who are HIV-seropositive and not on anti-retroviral therapy and who otherwise meet the inclusion/exclusion criteria will be eligible for the study Seropositive for the human immunodeficiency virus (HIV) Known to be human immunodeficiency virus (HIV) seropositive Patients who are seropositive for human immunodeficiency virus (HIV) Known seropositive for human immunodeficiency virus (HIV); HIV testing is not required; hepatitis testing is not required Seropositive for human immunodeficiency virus (HIV). Seropositive for human immunodeficiency virus (HIV). Subjects known to be seropositive for HIV or for HTLV-I Patients seropositive for HIV-1 or -2 Patients seropositive for the human immunodeficiency virus (HIV) Patients who are seropositive for human immunodeficiency virus (HIV) Patients who are human immunodeficiency virus (HIV) seropositive Patients seropositive for the human immunodeficiency virus (HIV) Patients seropositive for the human immunodeficiency virus (HIV) Positive human immunodeficiency virus (HIV) or human T-cell lymphotrophic virus (HTLV)-1 serology Negative human T-lymphotropic virus (HTLV)-1 and 2 antibodies. EXCLUSION - PROCUREMENT: Active infection with human immunodeficiency virus (HIV) or human T-lymphotropic virus (HTLV) PROCUREMENT EXCLUSION: Active infection with human immunodeficiency virus (HIV) or human T-cell leukemia virus (HTLV) (can be pending at this time) No known history of human immunodeficiency virus (HIV) 1 and 2, human T-cell lymphotropic virus (HTLV)-I/II, and hepatitis B and C PART I: Negative serology for anti-human immunodeficiency virus (HIV)-1/2 and anti-human T-lymphotropic virus (HTLV) 1/2 Patients must have serum antibodies directed to human T-cell lymphotropic virus (HTLV)-1 Known infection with human immunodeficiency virus (HIV) or human T-cell leukemia virus 1 (HTLV-1) Seropositivity for human T-lymphotropic virus type 1 (HTLV-1). Known infection with human immunodeficiency virus (HIV) or human T-cell leukemia virus 1 (HTLV-1) Donors who are human immunodeficiency virus (HIV)-1, HIV-2, human T-lymphotropic virus (HTLV)-1, HTLV-2 seropositive or with active hepatitis B or hepatitis C virus infection Known infection with human immunodeficiency virus (HIV) or human T-cell leukemia virus 1 (HTLV-1) seropositive status Known infection with Human Immunodeficiency Virus (HIV) or Human T-lymphotropic Virus 1 (HTLV-1). Known infection with human immunodeficiency virus (HIV) or human T-cell leukemia virus 1 (HTLV-1) seropositive status Seronegative for human T-cell lymphotropic virus type 1 (HTLV-1) Positive results for the human T-lymphotrophic 1 virus (HTLV-1) Patients with human immunodeficiency virus (HIV) or human T-cell leukemia virus 1 (HTLV-1) are not eligible Subject has positive test result at the screening visit for one or more of the following:\r\n* Human T-cell lymphotropic virus (HTLV-1/2)\r\n* Anti-human immunodeficiency virus (HIV) 1 antibody (alpha-HIV-1) EXCLUSION CRITERIA FOR ENROLLMENT: Human immunodeficiency virus (HIV)-1/2 or human T-cell lymphotropic virus (HTLV)-1/2 positivity Human immunodeficiency virus (HIV) or human T-cell leukemia virus type (HTLV)1/HTLV2 (seropositivity and/or polymerase chain reaction [PCR] positivity) Active symptomatic fungal, bacterial and/or viral infection including evidence of infection with human immunodeficiency virus (HIV), human T-cell leukemia virus 1 (HTLV-1) seropositive status Subject has positive test result at the screening visit for one or more of the following: human T-lymphotropic virus (HTLV)-1/2 and/or anti-human immunodeficiency virus (HIV) 1 antibody (alpha-HIV-1) Known history of infection with human immunodeficiency virus (HIV) or human T cell leukemia virus 1 (HTLV-1) Active infection with human immunodeficiency virus (HIV) or human T-cell lymphotropic virus (HTLV) History of positive serology tests for human immunodeficiency virus (HIV) 1 and 2, human T cell lymphotropic virus (HTLV)-1, hepatitis B and C DONOR: HIV or human T-lymphotropic virus (HTLV) seropositive Patient seropositive for human immunodeficiency virus (HIV)-I/II; human T-cell lymphotropic virus (HTLV)-I/II Active infection with human immunodeficiency virus (HIV), human T-cell lymphotropic virus (HTLV), human T-cell lymphotropic virus (HBV), hepatitis C virus (HCV) (can be pending at this time) Patient seropositive for human immunodeficiency virus (HIV)-I/II; human t-lymphotrophic virus (HTLV) -I/II Seropositivity for human T-lymphotropic virus type 1 (HTLV-1) Human immunodeficiency virus (HIV)-1/HIV-2 or human T-lymphotropic virus (HTLV)-1/HTLV-2 seropositivity Patients with evidence of human immunodeficiency virus (HIV) seropositivity and/or positive polymerase chain reaction (PCR) assay, human T-cell leukemia virus type (HTLV)1/HTLV2 seropositivity Known human immunodeficiency virus (HIV) or human T-cell lymphotropic virus (HTLV) infection Participants with known infection with human immunodeficiency virus (HIV) or human T-cell leukemia virus 1 (HTLV-1) Participants with known infection with human immunodeficiency virus (HIV) or human T-cell leukemia virus-1 (HTLV-1) Patient is positive for human immunodeficiency virus (HIV) or human T-cell lymphotropic virus-1 (HTLV-1) Patient seropositive for human immunodeficiency virus (HIV)-I/II; human T-cell lymphotropic virus (HTLV)-I/II Active infections including human T-lymphotropic virus (HTLV) 1 and 2, and human immunodeficiency virus (HIV) 1 and 2 Patient seropositive for human immunodeficiency virus (HIV)-I/II; human T-lymphotrophic virus (HTLV)-I/II Seronegativity for human immunodeficiency virus (HIV), human T-cell lymphotropic virus (HTLV1), hepatitis Human T-lymphotropic virus (HTLV)-1/2 Patient seropositive for human immunodeficiency virus (HIV)-I/II; human T-cell lymphotropic virus (HTLV) -I/II Positive test results for human T-lymphotropic virus type I (HTLV 1) virus in endemic countries DONOR: Human immunodeficiency virus (HIV) or human T-lymphotrophic virus (HTLV) infection Known human immunodeficiency virus (HIV) or human T-lymphotropic virus, type I (HTLV-I) positive status Human immunodeficiency virus (HIV) or Human T Cell Lymphotropic Virus 1 (HTLV-1) infection Human immunodeficiency virus (HIV) or human T-lymphotropic virus (HTLV)-I/II Human immunodeficiency virus (HIV) infection or Human T Cell Lymphotropic Virus 1 (HTLV-1) infection Has a known human T-lymphotropic virus type 1 (HTLV) infection Known infection with human immunodeficiency virus (HIV) or human T-cell leukemia virus 1 (HTLV-1) Known infection with human immunodeficiency virus (HIV) or Human T-Cell Leukemia Virus 1 (HTLV-1) seropositive status Known history of human immunodeficiency virus (HIV) seropositive status or known infection with human T-cell leukemia virus 1 (HTLV-1) virus No known history of human immunodeficiency virus (HIV) 1/2, human T-lymphotropic virus (HTLV)-I/II Patients seropositive for Human T-Lymphotrophic Virus (HTLV)-I or -II Positive serology for human immunodeficiency virus (HIV) or human T-cell lymphotropic virus (HTLV) at any time prior to enrollment; The patient has known positive human immunodeficiency virus (HIV) or known active human t-cell lymphotropic virus (HTLV) I/II disease, whether on treatment or not.