PROSTVAC (PSA-TRICOM) in Preventing Disease Progression in Patients With Localized Prostate Cancer Undergoing Active Surveillance

Inclusion Criteria: * Biopsy-proven (consisting of \>= 10 tissue cores) adenocarcinoma of the prostate with cancer present in at least one biopsy core, either random or targeted, in the most recent biopsy * All prior biopsies must meet the following: =\< 50% of the total number of random biopsy cores positive for cancer * Gleason score =\< (3+4) * Clinical stage =\< T2a by digital rectal exam (DRE) * Biopsies performed at outside institutions should have Gleason score confirmed at the study site by a genitourinary (GU) pathologist to ensure eligibility * Pre-intervention biopsy tissue (most proximal to enrollment) with sufficient tumor tissue to cut 5-10 unstained slides confirmed to be available upon request * Screening serum PSA \< 20 ng/mL; for men treated with 5-alpha-reductase inhibitors (e.g., finasteride, dutasteride), PSA needs to be \< 10 ng/mL * Neutrophil count \>= 1,200/mm\^3 (\>= 1.2 k/uL) * Stable platelet count \>= 75,000/mm\^3 (\>= 75 k/uL) * Bilirubin =\< 1.5 mg/dL (or =\< 3.0 mg/dL for patients with Gilbert's syndrome) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x upper limit of normal (ULN) * Serum creatinine =\< 1.5 x ULN * Karnofsky \>= 70% * Must agree to use medically acceptable barrier and/or chemical method of contraception while on study and for at least one month following the last vaccine injection; should a participant's partner become pregnant or suspect she is pregnant while the participant is participating in this study, the study physician should be informed immediately; in the event a participant's partner becomes pregnant, the study sponsor may request additional information regarding the course of the pregnancy and if the pregnancy is carried to term, the birth of the child (i.e., the outcome of the pregnancy) * Ability to understand and the willingness to sign a written informed consent document * No planned prostate biopsies during the intervention until after the post-intervention biopsy * Men on stable doses of 5-alpha reductase inhibitors are eligible as long as there is no planned dose change while on study Exclusion Criteria: * Have had prior treatment for prostate cancer by surgery, irradiation, local ablative (i.e., cryosurgery or high-intensity focused ultrasound), or androgen-deprivation therapy * Patients who have prostate cancer with distant metastases * Have undergone treatment of hormone therapy, immunotherapy, chemotherapy and/or radiation for any malignancies within the past 2 years * Uncontrolled intermittent illnesses or medical conditions which, in the opinion of the treating physician, would make this protocol unreasonably hazardous for the patient; such illnesses/conditions may include, but are not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, symptomatic or unstable cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Positive for human immunodeficiency virus (HIV) or active infections for hepatitis B, and/or hepatitis C, based on medical history * Prior solid organ or bone marrow transplant * Immunodeficiency or splenectomy * Chronic immunosuppressive therapy within 30 days of screening * Inflammatory eye disease requiring steroid treatment within 28 days of screening * Chronic administration (defined as daily or every other day for continued use \> 14 days) of systemic corticosteroids within 28 days of the first planned dose of PROSTVAC-V/F; use of inhaled steroids, nasal sprays, and topical creams for small body areas is allowed * History of or active autoimmune disease including but not limited to autoimmune neutropenia, thrombocytopenia, or hemolytic anemia, systemic lupus erythematosus, Sjogren's syndrome, scleroderma, myasthenia gravis, Goodpasture's syndrome; persons with vitiligo are not excluded; Persons with well-controlled autoimmune endocrinopathies, e.g., diabetes mellitus, Graves' disease, Hashimoto's thyroiditis, Addison's disease are not excluded; persons with well-controlled rheumatoid arthritis, psoriatic arthritis and polymyalgia rheumatica are not excluded * Known allergy to eggs, egg products * Prior or concurrent eczema or other eczemoid skin disorders or active skin condition (acute, chronic, or exfoliative) that disrupts the epidermis; persons with psoriasis are not excluded except in cases of: * any active lesion * any active lesion in the previous 6 months that required treatment, either systemic or topical * any prior episode, at any time, extensive enough or severe enough as to require systemic treatment * Previous adverse reactions to smallpox vaccination * Unable to avoid close contact or household contact with the following high-risk individuals for three weeks after the day 1 vaccination or until the vaccination site heals completely: (a) children =\< 3 years of age, (b) pregnant or nursing women, (c) individuals with prior or concurrent extensive eczema or other eczemoid skin disorders, (d) individuals with other acute, chronic, or exfoliative skin condition, or (e) immunocompromised or immunosuppressed persons (by disease or therapy) * Participants may not be receiving any other investigational agents * History of allergic reactions attributed to compounds of similar chemical or biologic composition of PROSTVAC