Enzalutamide and Cabazitaxel in Treating Patients With Metastatic, Castration-Resistant Prostate Cancer

Inclusion Criteria:

* Metastatic CRPC
* Willing to provide a tumor sample via biopsy from a metastatic site of disease to be collected at screening if safe and feasible per discretion of treating investigator; adequate archival metastatic tissue can be used, if available, in lieu of baseline biopsy if done when patient had CRPC; patients without a site amenable to biopsy and lack of archival tissue may still join the study
* Evidence of prostate cancer progression by any of the following criteria: radiographic or PSA criteria, or symptomatic progression related to prostate cancer
* Castrate testosterone levels (\< 50 ng/dL) achieved by orchiectomy or maintenance on a luteinizing hormone-releasing hormone (LHRH) agonist or antagonist
* Histologic confirmation of original prostate cancer diagnosis per institutional standard; life expectancy of greater than 6 months
* Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
* Leukocytes \>= 3,000/mm\^3
* Absolute neutrophil count \>= 1,500/mm\^3
* Platelets \>= 100,000/mm\^3
* Total bilirubin within normal institutional limits (or \< 2 X the upper limit of normal in those with Gilbert's disease)
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 1.5 X institutional upper limit of normal
* Creatinine within less than the institutional upper limit of normal
* Creatinine clearance \>= 45 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal
* Subject agrees to use a double barrier method of birth control during the course of study treatment period with enzalutamide and/or cabazitaxel treatment and for at least 3 months after the study is discontinued

  * A double-barrier method of contraception involves the use of a condom in combination with 1 of the following: contraceptive sponge, diaphragm, or cervical ring with spermicidal gel or foam
  * Subject who has had a vasectomy at least 6 months prior to starting study treatment period and those whose female sexual partner(s) are more than 55 years of age and postmenopausal for at least 2 years or surgically sterile (tubal ligation, hysterectomy, or bilateral oophorectomy) agree to use at least a condom
* Ability to understand, and the willingness to sign, a written informed consent document, as well as comply with study requirements
* Must have appropriate wash out (\> 6 half-lives) of androgen receptor antagonists, 5 alpha reductase inhibitors or ketoconazole prior to the start of cycle 1; if the agent is not in the table below, the washout should be 2 weeks

  * Bicalutamide; approximate half-life: 6 days; washout period required: 36 days
  * Flutamide; approximate half-life: 6 hours; washout period required: 36 hours
  * Nilutamide approximate half-life: 4 days; washout period required: 24 days
  * Finasteride; approximate half-life: 8 hours; washout period required: 48 hours
  * Aminoglutethimide; approximate half-life: 15 hours; washout period required: 4 days
  * Ketoconazole; approximate half-life: 8 hours; washout period required: 48 hours

Exclusion Criteria:

* Prior chemotherapy for mCRPC prostate cancer; chemotherapy given neoadjuvantly, adjuvantly, or for hormone sensitive metastatic disease is permitted as long as the cancer did not progress on chemotherapy AND \> 6 months have elapsed
* Patients may not have received any other investigational agents within the last 14 days at the time of treatment start
* Patients may not have received enzalutamide or ARN-509 (another androgen receptor antagonist) in the past
* Patients may not have received cabazitaxel in the past
* Subject has clinical signs suggestive of high or imminent risks for pathological fracture, spinal cord compression and/or cauda equina syndrome
* History of severe hypersensitivity reaction (\>= grade 3) to docetaxel, polysorbate 80 containing drugs, or any of the capsule components of enzalutamide, including Labrasol, butylated hydroxyanisole, and butylated hydroxytoluene
* Concurrent or planned treatment with strong inhibitors or strong inducers of cytochrome P450 family 3, subfamily A, polypeptide 4/5 (3A4/5); (a one-week wash-out period is necessary for patients who are already on these treatments)
* Uncontrolled, intercurrent illness including, but not limited to, ongoing or active infection, uncontrolled diabetes, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
* Subject has a history of seizure or any condition that may predispose to seizure including, but not limited to, underlying brain injury, stroke in the past 6 months, primary brain tumors, brain metastases, prior seizures
* Subject has a history of unexplained loss of consciousness or transient ischemic attack within 12 months of treatment start
* Subject is unwilling to stop using herbal supplements that can affect the PSA, such as saw palmetto or prostate cancer (PC)-SPES
* Subject has another active malignancy other than non-melanomatous skin cancer (unless it is metastatic) or superficial bladder cancer
* Must not have a gastrointestinal condition that would interfere with absorption
* Subjects may not be on other therapies that affect hormone levels, such as estrogens, testosterones, ketoconazole during this study; however, megestrol for hot flashes is permitted