The reason why this concept works so well is that it mimics real life. In general, we are punished for stop behaviors and rewarded for start behaviors. If I am caught speeding (a stop behavior), I will be punished with a ticket and a fine. If I do well at my job (a start behavior), I am rewarded with a paycheck and possibly a bonus.
So when you are thinking about how to deal with a situation that needs a reward or punishment, try using these simple ideas: Stop behaviors = punishments and start behaviors = rewards.