What would make a 1987 Buick Lesabre T Stall when you hit the breaks?

When you are driving it is fine until you hit the breaks. It begins to run rough and stalls. One day we drove it a little over 10 miles and it stalled 6 timesWhat would make a 1987 Buick Lesabre T Stall when you hit the breaks?the brake booster is vacuum operated and when you hit the brakes the motor has a very bad vacuum leak. so have the brake booster checked.