Run out rules in cricket if one player doesn't run

If player A doesn't leave his ground (crease), then Player B is out. If both player has left the crease, then any player arriving at any crease earlier than other player is safe..

If the Batsmen have crossed in running, he who runs for the wick- et which is put down shall be out; if they have not crossed, he who has left the wicket which is put down shall be out. If a Batsman remains in his ground or returns to his ground and the other Batsman joins him there, the latter shall be out if his wicket is put down.

http://static.espncricinfo.com/db/ABOUT_CRICKET/LAWS/1980_CODE/LAW_38_RUN_OUT.html

If A player doesn't run then the player B (which reach at A's crease) declared as out in your case because player A doesn't left his crease. But if the ball hits the stumps at A's crease then no one considered as out.

Hope this is helpful.

1. If Player A - Does not leave the crease, Player B is out.
2. If both are out of the crease, the player closest to the opposite crease is considered Not-Out or vice-versa and NOT the player arriving at crease first. Example: Player A,B are out of the crease. Ball hits at B's crease, Player A is closest to the opposite crease; Player B is considered out.

Run Outs come under Law 38 - Cricket