Here's an example from a recent game in a regressive league I'm in
https://www.whatifsports.com/slb/Boxscore.aspx?gid=35228235&pid=1&pbp=0&tf=12.95
My regular first baseman Eddie Murray is pinch run for in the top of the eighth inning by Omar Moreno. In the bottom of the eighth, since Moreno doesn't have a first base fielding rating, he is replaced by Rick Monday, who is at the top of my first base defensive replacement hierarchy.
Then in the top of the 10th inning, Monday is pinch hit for by AAA Chad Butler. Butler has a fielding rating at first base, but is nowhere on the first base player rest or defensive replacement hierarchy. Butler remains in the game in the bottom of the 10th.
It's worth noting my defensive replacement hierarchy for first base is just Monday and Murray, so it's possible if I had another player who was still available listed there, that guy would have replaced Butler for the bottom of the 10th, but my guess is since the game was still tied and it wasn't a situation where automatic defensive replacements would be triggered, that Butler would have stayed in at first base regardless.