I was taught a couple of variations of this. The first one, you are on the right side of the break box or even over to the rail, you hit the one ball like you are cutting the one ball to the first or middle diamond on the foot rail. The cue ball cuts across the face of the one ball and goes over to the long rail below the side pocket and returns to the middle of the table. This cuts down the collisions with the cue ball and object balls and you never scratch in the side.
The other is a safety break when you are not making balls no matter what you do so you give up trying. It is the same except you cut across the one ball more toward the left side and the cue ball goes to the middle diamond on the long rail then the middle diamond on the foot rail. The one ball goes up the middle of the table and settles somewhere in the middle of the head rail. Your opponent is always going to push from there. Some days when it just ain't working you are better off responding to your opponents push than accepting your own break. At least you are going to get a look at the ball and you and your opponent are starting off on even ground, sort of.
The other is a safety break when you are not making balls no matter what you do so you give up trying. It is the same except you cut across the one ball more toward the left side and the cue ball goes to the middle diamond on the long rail then the middle diamond on the foot rail. The one ball goes up the middle of the table and settles somewhere in the middle of the head rail. Your opponent is always going to push from there. Some days when it just ain't working you are better off responding to your opponents push than accepting your own break. At least you are going to get a look at the ball and you and your opponent are starting off on even ground, sort of.