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NCAA Ruling
The NCAA rule book leaves no room for discussion on the situation.
Rule 3-1-2: The team may continue to play with fewer than five players when all other squad members are not eligible or able to play
Rule 3-4-14: A player who has been withdrawn or replaced by a substitute may reenter the game at the next opportunity to substitute, provided that the game clock has been properly started after the withdrawal or replacement.
Rule 4-51: Player: A player is one of five or fewer members of a team's personnel who is legally on the playing court to participate
Rule 4-65: Team Member: A team member is a member of the bench personnel who is in uniform and is eligible to become a player.
Based on those rulings, if this play were to happen in a college game, one of the four remaining players on the floor would have to shoot the free throws and they would play with 4 until the next opportunity to sub in the 5th player.
I don't know if the High School ruling is the same as I'm not sure of the language in the rule book.
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