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The ball becomes dead when time expires for a quarter or extra period (6-7-6). There is one exception to this, and that is if the ball is in flight on a try or tap for field goal (6-7 Exception A). In OP, the ball was not in flight on a try or tap for field goal when time expired for the quarter, so the ball became dead when the signal sounded indicating that time had expired.
A personal foul may be committed on an airborne shooter after the ball has become dead (4-19-1). However, an airborne shooter is defined as a player who has released the ball on a try for field goal or has tapped the ball and has not returned to the floor (4-1-1). A try for field goal is defined as an attempt by a player to score two or three points by throwing the ball into a team's own basket (4-41-2). Since a goal can only be made when a live ball enters the basket from above and passes through (5-1-1), and we have determined that the ball is dead, then the "shooter" in OP did not release the ball on a try for field goal. Since the "shooter" did not release the ball on a try for field goal, then the "shooter" did not become an airborne shooter. Therefore, since the ball is dead and the fouled player is not an airborne shooter, the contact is ignored unless ruled to be intentional or flagrant (4-19-1 Note). The fourth quarter ends when the signal sounds to indicate that time has expired in the quarter (5-6-2). Since the score was tied when the fourth quarter ended, an extra period shall be played (5-7-1).
If the contact is ruled to be intentional or flagrant, then a player technical foul has occurred (10-3-7) after the fourth quarter ended. The penalty for this foul will be administered to start the extra period (5-6-2 Exception 4) following a one-minute intermission (5-7-1). Any player or eligible substitute from the offended team may shoot the awarded free throws (8-3). Both free throws shall be attempted and the initial AP arrow shall be set in the direction of the opponent's basket when the ball is placed at the disposal of the thrower following the free throws (4-3-3b).
If the contact is not ruled to be intentional or flagrant, then the contact is ignored and no foul has occurred, as previously stated. The extra period will begin with a jump ball (6-2-2).
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