Ipilimumab in Combination With Androgen Suppression Therapy in Treating Patients With Metastatic Hormone-Resistant Prostate Cancer

Inclusion Criteria:

* Willing and able to give written informed consent
* Histologic diagnosis of adenocarcinoma of the prostate
* A PSA of \> 0.2 ng/ml after 6-18 months of androgen suppression therapy, which may consist of luteinizing hormone-releasing hormone (LHRH) agonist or antagonist alone or the combination of an LHRH agonist or antagonist plus an antiandrogen, such as bicalutamide; androgen suppression therapy will continue without interruption
* Radiographic evidence of regional or distant metastasis at the time of study enrollment or at the time of diagnosis
* White blood cell (WBC) \>= 2000/uL
* Absolute neutrophil count (ANC) \>= 1000/uL
* Platelets \>= 50 x 10\^3/uL
* Hemoglobin \>= 8 g/dL
* Creatinine =\< 3.0 x upper limit of normal (ULN)
* Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.5 x ULN for patients without liver metastasis
* Bilirubin =\< 3.0 x ULN, (except patients with Gilbert's syndrome, who must have a total bilirubin less than 3.0 mg/dL)
* No known active or chronic infection with human immunodeficiency virus (HIV), hepatitis B, or hepatitis C; patients should be assessed for high risk behaviors that may result in these infections, such as intravenous drug use or multiple sexual partners; the assessment should be noted
* Eastern Cooperative Oncology Group (ECOG) =\< 1
* Patients receiving any herbal product known to decrease PSA levels (i.e. saw palmetto and prostate cancer \[PC\]-SPES), or any immunosuppressive dose of systemic or absorbable topical corticosteroid (except prednisone up to 10 mg orally per \[q\] day, or its equivalent), must discontinue the agent for at least 2 weeks prior to screening; progressive disease must be documented after discontinuation of these products
* Patients receiving bisphosphonate therapy must have been on stable doses for at least 4 weeks with stable symptoms prior to the first infusion with ipilimumab
* Total testosterone \< 50 ng/ml, except in patients with prior orchiectomy, where testosterone does not need to be measured; patients must continue their LHRH agonist therapy throughout study duration
* Life expectancy \>= 6 months; this must be documented
* Patients who are sexually active with a partner who could become pregnant are to use an effective form of barrier contraception, such as condoms or a partner using oral contraceptive pills; persons of reproductive potential must agree to use an adequate method of contraception throughout treatment and for at least 8 weeks after ipilimumab is stopped
* If a patient enters the trial on androgen suppression therapy (AST) that consists of both an LHRH agonist and an oral antiandrogen, both agents should be continued throughout the study; if an antiandrogen is stopped prior to study entry, it should be stopped 4 weeks before for nilutamide and flutamide and 6 weeks before for bicalutamide to ensure that a withdrawal phenomenon does not interfere with interpretation of efficacy results

Exclusion Criteria:

* Radiation to any area of the body \< 28 days prior to randomization
* Any other active malignancy with the exception of adequately treated basal or squamous cell skin cancer or superficial bladder cancer
* Autoimmune disease: patients with a history of inflammatory bowel disease are excluded from this study, as are patients with a history of symptomatic disease (eg, rheumatoid arthritis, systemic progressive sclerosis \[scleroderma\], systemic lupus erythematosus, autoimmune vasculitis \[eg, Wegener's granulomatosis\]); motor neuropathy considered of autoimmune origin (e.g. myasthenia gravis, Guillain-Barre syndrome); those with immune-mediated skin toxicity (i.e. toxic epidermal necrolysis, Stevens-Johnson syndrome) will also be excluded
* Any underlying medical or psychiatric condition, which in the opinion of the investigator will make the administration of ipilimumab hazardous or obscure the interpretation of adverse events (AEs), such as a condition associated with frequent diarrhea
* Any non-oncology vaccine therapy used for prevention of infectious diseases (for up to 1 month before or after any dose of ipilimumab)
* A history of prior treatment with ipilimumab or prior cluster of differentiation (CD)137 agonist or cytotoxic T-lymphocyte-associated protein 4 (CTLA-4) inhibitor or agonist
* Concomitant therapy with any of the following: interleukin (IL)-2, interferon, or other non-study immunotherapy regimens; cytotoxic chemotherapy; immunosuppressive agents (over the counter \[OTC\]/herbal/prescribed); immunostimulant agents, other than the study agent; other investigational therapies; or chronic use of systemic corticosteroids (greater than prednisone 10 mg orally per day, or its equivalent)
* Prisoners or patients who are compulsorily detained (involuntarily incarcerated) for treatment of either a psychiatric or physical (i.e., infectious) illness