This idea is if your rival is a villian and steals the professors pokemon that is more powerful than yours at the beginning. Then, throughout the game, you encounter him a couple times and battle him for the Pokemon, but each time, right when you are about to defeat him, he cowardly runs away. Eventually he becomes the Pokemon champion. When you defeat him, the fourth Elite Four person comes in and asks about all the commotion. Your rival, with nowhere to run, releases his now fully evolved starter and tells it to run away. The starter uses Hydro Pump/Solarbeam/Fire Blast to create a hole in the wall, and runs into the wild. I don't know what would happen to your rival, but he would be dealt with. Finally, you are the Pokemon champion, but you now need to find the starter your rival let loose. It would be captured the same way as the Legendary Beasts/Lati@s. Once you capture it you can show the professor, and he will give you some sort of reward.
Another thought I had is if you had two rivals, the one that would be like May/Brendan would get the starter with a weakness to yours and the thief would get the one with an advantage over yours.