What happens if the ball is hit onto the non-striker's wicket?

Assuming nobody from the fielding side has touched the ball, nothing happens and nobody is out. If someone from the fielding side touches the ball, and it breaks the stumps with the non-striker (the other batsman) out of his ground (beyond the line on the ground in front of the stumps), then the non-striker is run out.

It's an unfortunate and frustrating way to get out, but it's happened to most of us at some stage.

The usual laws of run-outs apply here also

If the bowler(or any fielder) touches the ball( or the ball comes in contact with any part of the fielder) and the ball hits the stumps at non-striker end and

1. If the batsman is out of his crease then he is out

2. If the batsman is inside the crease then he is not out. The batsman can attempt to take runs if he wishes

If the fielder does not touch the ball then the batsman is not out. Again they can attempt to take runs.