We're in the middle of the World Series and my catcher got injured and will miss the rest of the series.
I have two players on the ML roster that are playoff eligible, but the game will not let me add them in the middle of a series.
So, I have to play short-handed and if my other player gets hurt I'm really in trouble?
What happens if three players get hurt, and I don't have enough to field 9 hitters?

Can't switch once a series starts. I always drop the number of pitchers I carry in the postseason, you're really noy going to need your 4th & 5th starters or bottom 2 relievers. I'll carry 11 pitchers and balance positional.

In all the years I've played I never faced this. I thought about dropping a pitcher and putting an extra PH type on the roster for the playoffs and decided not to in case of one of those 16 inning games wreaking havoc on my staff.
The problem is with catchers though...having an extra hitter is one thing and, if they're at least have reasonable fielding ratings can cover a number of positions. If you lose your catchers it's a significant problem.

I always carry 3 catchers in post season, or at least have an emergency one that's a positional players that might have 30ish pc. I think you're more apt to have an injury than a 15 inning game

I dunno I had a lot more long games than injuries this season, but I also tend to keep guys with higher health ratings (not that that seems to matter) and 20 Training. Anyway, from now on...I will carry a third catcher into the playoffs.