Mike,
Is the batter still at bat? If he cannot continue his at bat, and there are no eligible subs, he is called out.
Then, each time his spot in the order comes up, it is recorded as an out. If an eligible sub magically appears,
he can be placed into the batting order for the hurt player and life is good again.
I believe I had the same or similar question on my test. I'll check it tonight. I'm fairly certain I answered it correctly.