This article is helpful: https://www.mlb.com/news/abs-challenge-system-mlb-2026
In particular:
Can challenges affect runner placement?
Yes. Inevitably, there will be instances in which teams want to challenge a pitch that was called during a play while other things happened on the field. So the umpires will determine whether that call on the field had an impact on the subsequent behavior of the defenders and baserunners. The umpires will let stand any calls unaffected by the incorrect call.
As an example, say there is a runner at second with none out, and the batter is in a full count. The 3-2 pitch is thrown and called a ball, while the runner attempts to steal third. The runner beats the throw from the catcher and is called safe at third, but then the catcher challenges the ball call. Upon review, the pitch is revealed to be a strike. Rather than send the runner back to second base, the runner gets to remain at third, because the initial ball/strike call did not impact the catcher’s ability to try to throw him out. The batter is now out, but the runner is still safe.
Also note that if a catcher drops a pitch that is initially ruled a ball but is overturned for strike three, the batter is out without requiring the batter or first base to be tagged (as would be required in the event of a traditional dropped third strike).