In Order to "Break the Loop" you need to collect all the decipher fragments.
Once you have all of them. Complete mission 7, and you will be returned to mission 1. it will now be called, the end is only the beggining. Play up to mission 5, or go to the DNA screen and skip to it. Once you come to the end of mission 5, a golden bridge will let you cross to the exit door.
Congradulations! You just broke the loop. Happy 50G!!!