USSSA rule: (ASA is similar)
G. After hitting or bunting a ball, the bat hits the ball a second time while the
ball is on or over fair territory, or is on or over foul territory and, in the
Umpire?s judgment, had a chance to become a fair ball, the ball is dead, no
runner(s) advance and the batter is out.
EXCEPTION: If the bat and ball accidentally come in contact with each
other a second time while the batter is holding the bat in the batter?s box,
it is a foul ball.
NOTE: If the batter drops the bat and the ball rolls against the bat in fair
territory and, in the Umpire?s judgment, there was no intention to interfere
with the course of the ball, the batter is not out and the ball is live and in
play.
NFHS case study example:
B1 swings and (a) hits the ball which strikes home plate and bounces up hitting the bat while the batter is in the batter's box; (b) after laying down the bat and running to first, the ball hits the bat in fair territory; or (c) while advancing to first, drops the bat in fair territory and the bat, while still moving, hits the ball.
RULING: A foul ball in (a). The ball remains live in (b). In (c), the batter is out and the ball is dead.