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 participatin…