This one used to happen to me a lot - I was much better on groundwork than standing, so my opponents, who knew this and were no dummies, would try to go to the edge of the mat. Their strategy was to attack at the edge and if the attack failed, either go out of bounds before we hit the mat or, if we did go to the mat, get out of bounds immediately. My strategy was not to let them do that.
How many times have you seen these things happen when players are at the edge of the mat:
One steps out and gets a penalty. A little while later, he steps out again, gets another penalty, can't score to catch up and loses the match.
In trying to avoid going out of bounds, one player moves into a bad position and gets thrown.
One player lets up, thinking they are out of bounds. The other player attacks and slams him/ her.
Incidentally, there was a pattern a while back, particularly among players from one particular place, who would deliberately attack when they knew they were out of bounds. Their reasoning seemed to be that if the referee called it correctly out of bounds, at worst nothing happened, and at best they would get a score. Somewhere in between there was a third possibility that the referee would call the throw out of bounds but the other player would be shaken up enough, either physically or mentally, from being thrown that when they went back in bounds and started up again the "cheating" player would have an advantage and win. It really is against the rules to deliberately throw your opponent after the referee has called matte but usually referees give you the benefit of the doubt that you didn't hear them.
Of course, there is a fourth option. I started coaching the players I worked with that whenever the referee called break when they went out of bounds to stop attacking and be ready. If the opponent attacked, they were to counter and slam the person into the mat as hard as they could. I never cheated and I never teach anybody to cheat. But that doesn't mean you have to put up with cheap shots. Consider it giving the person a lesson and doing the community a favor.
As for practice, this week we did corner drills where players are at the edge of the mat and have to throw or get away from the edge without getting a penalty or getting scored on.