Enzalutamide and Mifepristone in Treating Patients With Metastatic Hormone Resistant Prostate Cancer

Inclusion Criteria: * Histologically or cytologically confirmed prostate cancer * Evidence of castrate testosterone level \< 50 ng/dL (or surgical castration) * For Phase I portion of the study: evidence of disease progression: * 2 or more new lesions on bone scan or * Progressive disease on computed tomography (CT)/magnetic resonance imaging (MRI) according to Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria or * Rising PSA: PSA evidence for progressive prostate cancer consists of a minimum PSA level of at least 2 ng/ml, which has subsequently risen on at least 2 successive occasions, at least 2 weeks apart * For Phase II portion of the study: * Subjects must be on enzalutamide for metastatic CRPC and within the first 12 weeks of enzalutamide at 160mg/day * Record of subject's enzalutamide start date and baseline PSA (within 28 days of starting) before starting enzalutamide available * Subjects must have documented clinically stable disease or better during the screening period of the study as defined by all of the following: * PSA =\<1.25 times the PSA at start of enzalutamide * Lack of radiographic progression as defined by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 and Prostate Cancer Working Group Criteria * Clinically stable as confirmed by treating physician * Any prior therapy for castrate disease is acceptable except prior specific cytochrome P450 family 17 (CYP17) antagonists (e.g. abiraterone acetate, orteronel) or prior second generation AR antagonists (e.g. enzalutamide or ARN509) which are excluded other than enzalutamide as specified for phase II portion; a minimum washout of 28 days for any other anticancer therapy prior to first dose of study drug is required (only applicable for phase I) * Any other radiotherapy or radionuclide require 28-day washout prior to first dose of study drug * Denosumab or zoledronic acid are allowed * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Total bilirubin =\< 1.5 x the upper limit of normal * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Therapy with other hormonal therapy, including any dose of megestrol acetate (Megace), finasteride (Proscar), dutasteride (Avodart), or any herbal product known to decrease PSA levels (e.g., saw palmetto and PC-SPES), or any systemic corticosteroid within 2 weeks prior to first dose of study drug * Inability to swallow capsules or known gastrointestinal malabsorption * History of other malignancies, with the exception of: adequately treated non-melanoma skin cancer, adequately treated superficial bladder cancer, stage 1 or 2 solid tumor malignancies who are without evidence of disease, or other solid tumors curatively treated with no evidence of disease for \>= 5 years from enrollment * Blood pressure that is not controlled despite \> 2 oral agents (systolic blood pressure \[SBP\] \> 160 and diastolic blood pressure \[DBP\] \> 90 documented during the screening period with no subsequent blood pressure readings \< 160/100) * History of seizure disorder or active use of anticonvulsants * Corrected QT interval (QTc) on electrocardiogram (EKG) \> 450 msec * Serious intercurrent infections or non-malignant medical illnesses that are uncontrolled * Active psychiatric illness/social situations that would limit compliance with protocol requirements * New York Heart Association (NYHA) class II, NYHA class III, or IV congestive heart failure (any symptomatic heart failure) * Concurrent therapy with strong inhibitors or inducers of cytochrome P450 family 3, subfamily A, polypeptide 4 (CYP3A4) or cytochrome P450 family 2, subfamily C, polypeptide 8 (CYP2C8) due to concerning possible drug-drug interactions