"There's the possibility of the person who's been bullied and found their strength then becoming a bully"

I'd reckon it's unlikely. Certainly, in my case, having been the kid that was bullied, and knowing what a crock of shit it is to be a bully's victim, a bully was the last thing I wanted to be. I couldn't be that ugly - it was (and is) anathema to me.

I don't recall anyone I know who was bullied becoming a bully themselves. Stronger, more self-assured certainly, but a bully? Nope.