Additional Study Information: This study aims to investigate ADXS-504 as a possible treatment for biochemically recurrent prostate cancer. ADXS-504 is a type of cancer treatment that is designed to stimulate your immune system to attack prostate cancer cells. ADXS-504 is made of bacteria that have been weakened to remove their ability to cause an infection. The bacteria have also been genetically altered so that they produce proteins that may be present in prostate cancer cells. When these proteins and other substances from the bacteria are released into a patient's body, it looks like an infection to the immune system, and the immune system launches an attack against it, but the attack is actually against any cancer cells that have those proteins and may lead to destruction of the cancer cells.