Okay, here we go!!!
Speaking ASA.
Rule 8.8.D The runner is out..."when the runner physically passes a preceding runner before that runner has been put out."
Note, it says a PRECEDING runner! Therefore, the person called out is the former trail runner. There is no caveat requiring the ball to be dead. The POE does indeed mention a live ball, but I believe this is for the purpose of demonstrating what occurs, the runner is out and the ball remains live.
In the 2001 ASA Umpire Clinic Guide, there is no mention of the ball's status concerning this rule.