Brentuximab Vedotin After Donor Stem Cell Transplant in Treating Patients With Hematologic Malignancies

Inclusion Criteria: * Patients must have a cluster of differentiation (CD)30+ malignancy, with CD30 positivity demonstrated either at time of original diagnosis or at any subsequent time point * Patients must have undergone allogeneic HCT from a related or unrelated donor; acceptable donors include: * Related donors: genotypically or phenotypically identical by serological typing for human leukocyte antigen (HLA)-A, -B, -C, and at the allele level for -DRB1 and -DQB1 * Unrelated donors: Fred Hutchinson Cancer Research Center (FHCRC) matching allowed will be grade 1.0 to 2.1: matched for HLA-A, -B, -C, -DRB1 and -DQB1 by high-resolution typing * For all donors, a single allele disparity will be allowed for HLA-A, -B, or -C as defined by high-resolution typing * Patients with HLA-haploidentical donors are not eligible * Patients must have documented post-transplant donor CD3+ chimerism of \> 50% in sorted peripheral-blood CD3+ cells * Patients must be at least 28 days out from allogeneic HCT at the time of enrollment; in general, patients should be no more than 60 days out from allogeneic HCT at time of enrollment; however, patients more than 60 days out from allogeneic HCT may be considered for enrollment in discussion with the protocol investigator (Dr. Maloney) * Patients must be enrolled on an FHCRC non-myeloablative allogeneic transplant protocol (not standard treatment plan); for eligibility purposes, "non-myeloablative" is defined here as conditioning therapy consisting of =\< 4 Gy total body irradiation, with or without fludarabine * Patients with prior exposure to brentuximab vedotin are eligible for enrollment on this trial, regardless of previous disease response * Women of childbearing age and men with female partners of childbearing age must be willing and able to use an effective method of contraception during the study and for at least 30 days after the last study dose of brentuximab vedotin * Patients must be able to give informed consent Exclusion Criteria: * Patients who are seropositive for human immunodeficiency virus (HIV) * Women who are pregnant or breast-feeding * Patients with moderate to severe peripheral neuropathy (grade 2 or higher); patients with a history of moderate/severe peripheral neuropathy may be enrolled if their neuropathy improves to =\< grade 1 at the time of enrollment * Patients with significant hepatic dysfunction, as manifested by a total serum bilirubin \> 4.0 g/dL; or clinical evidence of decompensated hepatic failure; or clinical evidence of decompensated portal hypertension * Patients with an absolute neutrophil count of \< 1,000 cells/mm\^3 * Patients with Eastern Cooperative Oncology Group (ECOG) performance status of \> 2 * Patients with a serum creatinine \> 3.0 mg/dL * Patients with known hypersensitivity to brentuximab vedotin or any excipient contained in the drug formulation * Patients currently receiving treatment with other systemic anti-neoplastic or investigational agents targeting their CD30+ hematologic malignancy * Patients with active and uncontrolled infection not responding to appropriate treatment should be discussed with the study investigator (Dr. Maloney) before enrollment * Patients who have received donor lymphocyte infusion for low donor chimerism or pending graft rejection are not eligible