Biomarker-Driven Therapy With Nivolumab and Ipilimumab in Treating Patients With Metastatic Hormone-Resistant Prostate Cancer Expressing AR-V7

Inclusion Criteria: * Histologically or cytologically confirmed adenocarcinoma of the prostate * Metastatic disease as defined by two or more bone metastases confirmed by bone scintigraphy or radiographic soft tissue metastasis * Detectable circulating tumor cells (CTCs) with detectable AR-V7 splice-variant by reverse transcriptase (RT)-polymerase chain reaction (PCR) For second cohort (amendment 1): The most recent therapy must be enzalutamide and enzalutamide will be continued for study duration despite progressive disease. The minimum required dose of Enzalutamide at enrolment should be no less than 80 mg once daily. * Known castration-resistant disease, defined according to Prostate Cancer Working Group 2 (PCWG2) criteria as: * Castrate serum testosterone level: =\< 50 ng/dL (=\< 1.7 nmol/L) * Subjects who have failed initial hormonal therapy, either by orchiectomy or by using a gonadotropin-releasing hormone (GnRH) agonist in combination with an anti-androgen, must first progress through antiandrogen withdrawal prior to being eligible; the minimum timeframe to document failure of anti-androgen withdrawal will be four weeks * Serum PSA progression defined as two consecutive increases in PSA over a previous reference value within 6 months of first study treatment, each measurement at least one week apart; serum PSA at screening \>= 2 ng/mL OR * Documented bone lesions by the appearance of two or more new lesions by bone scintigraphy OR * Bidimensionally-measureable soft tissue metastatic lesion assessed by computed tomography (CT) or magnetic resonance imaging (MRI) * Karnofsky performance status (KPS): \>= 70% within 14 days before start of study treatment (Eastern Cooperative Oncology Group \[ECOG\] =\< 1) * Life expectancy: at least 6 months * White blood count (WBC) \>= 2000/uL * Neutrophils \>= 1500/uL * Platelets \>= 100 x10\^3/uL * Hemoglobin \> 9.0 g/dL * Serum creatinine =\< 1.5 x upper limit of normal (ULN) or creatinine clearance (CrCl) \>= 40 mL/min (if using the Cockcroft-Gault formula) * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 3 x ULN * Total bilirubin =\< 1.5 x ULN (except subjects with Gilbert syndrome, who can have total bilirubin \< 3.0 mg/dL) * Men who are sexually active with women of childbearing potential (WOCBP) must use any contraceptive method with a failure rate of less than 1% per year; men receiving nivolumab and who are sexually active with WOCBP will be instructed to adhere to contraception for a period of 31 weeks after the last dose of investigational product * WOCBP is defined as any female who has experienced menarche and has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy) or who is not postmenopausal; menopause is defined clinically as 12 months of amenorrhea in a woman over 45 in the absence of other biological or physiological causes; in addition, women under the age of 55 must have a documented serum follicle stimulating hormone (FSH) level less than 40 mIU/mL * No evidence (within 5 years) of prior malignancies (except successfully treated basal cell or squamous cell carcinoma of the skin) * The subject is willing and able to comply with the protocol, and agrees to return to the hospital for follow-up visits and examination * The subject has been fully informed about the study and has signed the informed consent form and, where appropriate, Health Insurance Portability and Accountability Act (HIPAA) authorization for release of personal health information * NOTE: HIPAA authorization may be included in the informed consent or obtained separately Exclusion Criteria: * Has received an investigational therapeutic drug within the last 4 weeks prior to start of study treatment, or is scheduled to receive one during the treatment period * Has received external radiotherapy within the last 4 weeks prior to start of study treatment * Previous therapy with antiandrogens within 4 weeks * Patients should be excluded if they have had prior systemic treatment with an anti-programmed cell death protein 1 (PD-1), anti-PD-L1, anti-programmed cell death 1 ligand 2 (PD-L2), anti-cytotoxic T-lymphocyte-associated protein 4 (CTLA-4) antibody, or any other antibody or drug specifically targeting T-cell costimulation or immune checkpoint pathways * Symptomatic metastatic disease with signs of rapid progression per investigator's clinical judgment * Concurrent use of other anticancer agents or treatments, with the following exceptions: * Ongoing treatment with luteinizing hormone-releasing hormone (LHRH) agonists or antagonists, denosumab (Prolia) or bisphosphonate (eg, zoledronic acid) is allowed; ongoing treatment should be kept at a stable schedule; however, if medically required, a change of dose, compound, or both is allowed * Any treatment modalities involving major surgery within 4 weeks prior to the start of study treatment * Symptomatic nodal disease, i.e. scrotal, penile or leg edema (\>= Common Terminology Criteria for Adverse Events \[CTCAE\] grade 3) * Patients are excluded if they have active brain metastases or leptomeningeal metastases; subjects with brain metastases are eligible if metastases have been treated and there is no magnetic resonance imaging (MRI) evidence of progression for at least 4 weeks after treatment is complete and within 28 days prior to the first dose of nivolumab administration; there must also be no requirement for immunosuppressive doses of systemic corticosteroids (\> 10 mg/day prednisone equivalents) for at least 2 weeks prior to study drug administration * Patients should be excluded if they have an active, known or suspected autoimmune disease (e.g. inflammatory bowel disease, rheumatoid arthritis, autoimmune hepatitis, lupus, celiac disease); subjects are permitted to enroll if they have vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger * Patients should be excluded if they have a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration; inhaled or topical steroids and adrenal replacement doses \> 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease * Permitted therapies include topical, ocular, intra-articular, intranasal, and inhalational corticosteroids (with minimal systemic absorption); physiologic replacement doses of systemic corticosteroids are permitted, even if \> 10 mg/day prednisone equivalents; a brief course of corticosteroids for prophylaxis (eg, contrast dye allergy) or for treatment of nonautoimmune conditions (e.g. delayed-type hypersensitivity reaction caused by contact allergen) is permitted * Drugs with a predisposition to hepatoxicity should be used with caution in patients treated with nivolumab-containing regimen * Patients should be excluded if they have a positive test for hepatitis B virus surface antigen (HBV sAg) or hepatitis C virus ribonucleic acid (HCV antibody) indicating acute or chronic infection * Patients should be excluded if they have known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS) * Allergies and adverse drug reaction * History of allergy to study drug components * History of severe hypersensitivity reaction to any monoclonal antibody * Other primary tumor (other than castration-resistant prostate cancer \[CRPC\]) including hematological malignancy present within the last 5 years (except non-melanoma skin cancer or low-grade superficial bladder cancer) * Has imminent or established spinal cord compression based on clinical findings and/or MRI * Any other serious illness or medical condition that would, in the opinion of the investigator, make this protocol unreasonably hazardous, including, but not limited to: * Any uncontrolled infection * Cardiac failure NYHA (New York Heart Association) III or IV * Crohn's disease or ulcerative colitis * Bone marrow dysplasia * Known allergy to any of the compounds under investigation * Unmanageable fecal incontinence