If an official discovers the injury, the coach cannot buy his player back in by using a timeout. See Casebook 3.5.10 Situation A.
The rule also states that the player must stay out for one down. a down is defined as, "A down is action which starts with a legal snap (beginning a scrimmage down) or when the ball is kicked on a free kick (beginning a free-kick down). A down ends when the ball next becomes dead."
If a live ball foul occurs during the next down and A will repeat that down, the previously injured player can come back in since a down has been played. Note that this would only occur to live ball fouls. If a dead ball foul occurs, then the snap or kick never happened and the injured player will have to wait.
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