Foul on a shot that would not count?

[Berkut]

Is it possible to have someone shooting free throws for a foul on a shot that would not count?

A1 has the ball with time expiring. After he starts his shot, but before the ball is released, they are fouled. Before the shot leaves their hand, the buzzer sounds.

I think this means that we have a shot that had their been no foul, would not have counted, but it doesn't matter - there was a foul on a shot before time expired.

Mechanically, how would you handle this, if say the lead (2 man) had the foul while the trail is potentially waving off the shot? Would you make sure to put time back on the clock, or just shoot free throws with the lane cleared and 0.0 on the clock?