Here's my rant on how this could be possible (don't flame me >____>)
Let's say at the end of Bully/Canis Canem Edit, Jimmy's last chance to end the Bullies for good is to fight and defeat Russell. He ends up going home and is actually happy, changed from his old ways of bullying and such by meeting new friends. He, his mom, and his step-dad live happily ever after.
HOWEVER, let's say in an ALTERNATE timeline, Jimmy ends up KILLING Russell by accident. In turn, he escapes and begins a life of crime under the name James (Jimmy) Earl Cash, getting a wife and having kids. A young man, fascinated by this specimen, tracks down and captures Jimmy, beginning the Manhunt game.