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Girls stay with abusive guys is that those abused girls only know how to be with abusive guys. That's either how they were raised or that is the kind of relationship that they get drawn into subconsciously. Also, guys are stronger and more aggressive, so are more likely to be able to abuse, not that girls can't abuse guys though.
Sometimes girls stay with abusive guys because the girls don't see the abusive side of the guy most of the time. The girl is drawn in by his "sweetness", charm, and good looks. Even when he does abuse her, she thinks that he did it "just this once (or twice or even more)". Also, sometimes those girls think that they lose more than they gain if they just leave the guy, and so they put up with the abuse. Finally, sometimes being with the guy is their only choice, especially if they bought a house together or already have a child.
I doubt that if a girl leaves her boyfriend, he will do something to her. It is possible, but doesn't always happen. If the abusive boyfriend goes after the girl, then he will probably go to jail (if he does something wrong).