This pilot clinical trial studies targeted biopsies in determining response in patients with prostate cancer undergoing high-dose-rate brachytherapy (a type of radiation therapy in which radioactive material sealed in needles, seeds, wires, or catheters is placed directly into or near a tumor). Studying tumor tissue obtained before and after treatment may help doctors understand changes in a pathway that looks at how deoxyribonucleic acid (DNA) is repaired after it is damaged and to see if there are differences in the prostate tissue prior to and after starting androgen deprivation therapy.