I have more information regarding this issue. It appears to only happen when you are in a match or training scenario. If you are in menus then you can run another app and return without a problem.
It also does not matter how long you let ufc 3 run in the background before it crashes. I just tested this. Started a fight, opened an app, then immediately returned to the game. Within seconds, the fighters were glitched and frozen. It was not long after that my Xbox froze and soon shutdown on it's own.
This is probably very damaging to the machine and needs to be looked into immediately. Please address this issue and advise.