subsitution
 

A1 is in the game. B2 is fouled and gets to shoot free throws. A6 subs A1 out of the game.
A) B2 shoots the 1st free throw. A1 goes to the table to report back into the game. The official beckons A1 to enter the game. The ball is at B2 disposal and an Official notices that A1 is in the game.
B) B2 shoots the 1st free throw. A1 goes to the table to report back into the game. The official beckons A1 to enter the game. B2 makes the 2nd free throw and Team A has the ball at their disposal and an Official notices A1 in the game.
C) B2 shoots the 1st free throw. A1 goes to the table to report back into the game. The official beckons A1 to enter the game. B2 misses the 2nd free throw and Team A has rebounded the ball and at their disposal and an Official notices A1 in the game.

Does A1 stay in the game? Or is A1 removed?

Huh??

Are you asking if a player - A1 in this case - can be substituted for and then return to the game during the same dead ball period? If B is shooting two, A1 won't even be replaced until after the first shot. If one and one, he will be replaced before the first shot.

I'm pretty sure if A1 is subbed out, the clock must move before he or she can be subbed back into the game.

On a 2 shot foul, no subs should enter until after the first FT attempt. So A1 couldn't be taken/sub'ed out before the 1st shot and then let back in after the first shot.

In A and B, blow the whistle, stop play, and have A1 replaced and inform the coach he must wait until the clock runs.

In C, it's too late. Clock has already started running anyway. Play on.

Sure he could.
Let's say A6 is waiting to sub when the foul occurs. During the play, B3 was injured and replaced prior to the first shot. You would then allow A6 to come in as well.

A substitute becomes a player when he/she legally enters the court. If entry is not legal, the substitute becomes a player when the ball becomes live. Every one of your senaroes has the ball live....sooo refer to case book play 3.3.3 Situation B

I'm still not even sure if I understand what you're asking, but in each of your scenarios an official beckoned A1 into the game, so why should it be a surprise that they notice A1 in the game thereafter? If you're talking about an illegal substitution, then that is handled when they notice A1 trying to re-enter the game. Once they've entered the game, or the ball becomes live, they're there to stay...

The difference here, though, is that A1 is ineligible to play until the clock has run. He's not an illegal substitution. I think it's different.

Not correct (by rule). Ball is at their disposal, and is therefore a live ball. At this point A1 becomes a legal player.

well that's a different post.

Looks to me like Indiana got it right - A1 stays because the "illegal substitute" has become a player once the ball has become live. That said, I haven't opened up my books today...

Most posters didn't understand that you were asking whether A1 should be removed because the officials made the mistake of allowing him/her back in the game before he/she was legally able to re-enter.

Remember This ...
 

You don't have to play a tick, but, you do have to sit a tick.