[JetMetFan]

Here's NFHS 10-5-2:

The head coach shall replace or remove a disqualified/injured player, or player directed to leave the game, within 20 seconds when a substitute is available.

and NCAA 10-4-5/10-6-2g

The head coach shall replace a disqualified or injured player within 20
seconds when a substitute is available.

It's in the penalty section but both codes specify replacing a disqualified player when a substitute is available.

I had this happen in a D-3 game last season. The home team had five players. One fouled out about 10 minutes into the second half. The coach asked for the 20 seconds and the official closest to her said "no, you don't have any subs" and we played on. I know we want to be charitable at times but there really isn't any gray area given the way the rule is written. Besides, we're just opening up a can of worms in terms of dealing with the other coach.

As for the coach potentially saying there's another player in the locker room, let's think: before the game don't we tell the scorekeeper to write down the name of anyone who might show up/play? I know I do. In that game where the team had five players we asked beforehand if they thought anyone else would show. What I'm saying is a response like "there's another player in the locker room" shouldn't even be on the table. We should know if someone has a chance of showing up.