If S1, an illegal substitute, scores and a third out occurs while transitioning to a new inning, what happens?

When an illegal substitute, such as S1, enters the game and subsequently scores before a third out occurs, the situation is governed by specific rules regarding illegal substitutions. In this case, since S1 is considered an illegal player, their actions on the field are not valid.

When the third out happens while transitioning to a new inning with an illegal player who has scored, the score does not count because S1's participation in the play is deemed illegal. This means not only is S1 called out, but the run they scored is nullified. The rules are structured this way to maintain fairness and integrity in the game, ensuring that only players eligible to participate are allowed to contribute to the score. Thus, the outcome of the play is effectively negated due to S1's illegal status in the game.

Therefore, since the illegal substitute's actions lead to their out and invalidate any runs scored during their illegal participation, it's clear why the answer is that S1 is called out and the run does not count.