Cabazitaxel and Prednisone in Treating Patients With Metastatic Hormone-Resistant Prostate Cancer

Inclusion Criteria: * Histologically confirmed prostate adenocarcinoma * Metastatic disease * Able and willing to provide informed consent and to comply with the study procedures * Castration resistant disease defined as evidence of radiological and/or prostate specific antigen (PSA) progression despite castrate levels of testosterone (serum testosterone \< 50 ng/dL \[1.7 nmol/L\]); for PSA progression, there must be at least 2 sequential rises at a minimum of 1-week intervals; the first PSA value must be \>= 4 (Prostate Cancer Working Group 2 \[PCWG2\] criteria) * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * At least 21 days have passed since completing radiotherapy (exception for radiotherapy: at least 7 days since completing a single fraction of =\< 800 cGy to a restricted field or limited-field radiotherapy to non-marrow bearing area such as an extremity or orbit) at the time of registration * At least 21 days have passed since receiving any investigational agent at the time of registration * At least 21 days have passed since major surgery * Neuropathy =\< grade 1 at the time of registration * Has recovered from all therapy-related toxicity to =\< grade 2 (except alopecia, anemia and any signs or symptoms of androgen deprivation therapy) at the time of registration * Poor prognosis disease as defined by any of the following: * PSA nadir \>=4.0, or * Gleason score 8-10, or * Time from ADT initiation to CRPC of =\< 16 months * Hemoglobin \>= 90 g/L * Neutrophils \>= 1.5 x 10\^9 /L * Platelets \>= 100 x 10\^9/L * Aspartate aminotransferase (AST) \< 1.5 x upper limit of normal (ULN) * Alanine aminotransferase (ALT) \< 1.5 x ULN * Bilirubin =\< 1.0 x ULN (exceptions for Gilbert's syndrome) * Creatinine =\< 1.5 x ULN Exclusion Criteria: * Prior therapy with cabazitaxel or to other drugs formulated with polysorbate 80 * Prior taxanes for CRPC * Prior enzalutamide, abiraterone or ketoconazole * Other condition, illness, psychiatric condition, or laboratory abnormality that may increase the risk associated with administration of cabazitaxel, study participation, or may interfere with the interpretation of study results and in the judgment of the investigator would make the patient inappropriate for entry into this study * Histologic evidence of small cell/neuroendocrine prostate cancer * Patients with reproductive potential who do not agree to use accepted and effective method of contraception during the study treatment period and up to 6 months after the last administered dose; the definition of "effective method of contraception" will be based on the investigator's judgment