Brentuximab Vedotin in Treating Patients With CD30+ Malignant Mesothelioma That Cannot Be Removed by Surgery

Inclusion Criteria: * Voluntary written informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care * Female subject is either: a. post-menopausal for at least one year before the screening visit; or b. surgically sterilized; or c. willing to use an acceptable method of birth control (i.e., a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence) for the duration of the study and at least 6 months after the last dose of brentuximab vedotin * Male subject, even if surgically sterilized (i.e., status postvasectomy), agrees to use an acceptable barrier method for contraception (condom with a spermicidal agent), or completely abstain from heterosexual intercourse during the entire study treatment period through 6 months after the last dose of brentuximab vedotin * Absolute neutrophil count (ANC) \> 1500/mm\^3 * Platelets \> 100,000/mm\^3 * Hemoglobin (Hgb) \> 8.5 g/dL * Total bilirubin =\< 1.5 x upper limit of normal (ULN) * Serum glutamic-oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) and serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) \< 3 x ULN; AST and/or ALT may be up to 5 X ULN if with known liver metastases (mets) * Calculated creatinine clearance must be \>= 30 mL/minute * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Pathologic diagnosis of malignant mesothelioma (any primary site is acceptable, any histology is acceptable) * Have unresectable malignant mesothelioma (any histology) * Positive CD30+ immunohistochemical expression * Any line of prior therapy - patients may be chemo-naive or chemo-refractory (any line) * Patients must have measurable disease by modified Response Evaluation Criteria in Solid Tumors (RECIST) or RECIST; examinations for assessment of measurable disease must have been completed within 28 days prior to registration Exclusion Criteria: * Radiation therapy to more than 25% of the bone marrow; whole pelvic radiation is considered to be over 25% * Prior allogeneic bone marrow or organ transplantation * Female subject who is pregnant or breast-feeding; confirmation that the subject is not pregnant must be established by a negative serum beta-human chorionic gonadotropin (B-hCG) pregnancy test result obtained during screening; pregnancy testing is not required for post-menopausal or surgically sterilized women * Patient has received other investigational drugs with 14 days before enrollment * Serious medical or psychiatric illness likely to interfere with participation in this clinical study * No prior history of malignancy within 2 years, unless cured of a skin cancer or a stage I-III solid tumor; no prior hematologic malignancy within 3 years * Known hypersensitivity to brentuximab vedotin components * Persons who are incarcerated at time of enrollment (e.g., prisoners) or likely to become incarcerated during the study