Awarded bases to an injured runner

[UmpireErnie]

My play in the thread "irritating parent" caused me to think about how to handle this.

Take this example. Tie score, bottom of the inning, two outs. Runner coming home slides into F2 who is blocking the plate with the ball so on OBS...yet. Runner slides into tag and ball comes out. Runner is hurt but still tries to move to home plate but his blocked by F2 who no longer has the ball. Now we have OBS. Runner is tagged; dead ball, runner awarded home for what would be game winning run. But she is hurt and is now just laying on the ground.

Coaches come over to attend to injured runner. Defense is leaving the field but only 2 or 3 have even crossed the foul line when runner is helped to her feet and helped off field with HC and assistant coach on either side of her.

Def coach runs up and says "Appeal she never touched home".

My question in all of this is that we are supposed to give offense an opportunity to complete baserunning duties, and bases awarded to an injured runner may be run by an eligible sub. So at what point to we decide that offense has had the opportunity to give us a sub and have the sub touch home? I could see in this senario the off coach getting all the way to the dugout with injured runner then turning around to come give me a sub.

My first thought would be to not accept the appeal yet until I felt that the off coach was not coming to me with a sub. I don't want to say or do anything to tip off either side.