Substitute player for the foul shooter

[johnyd]

Please refresh my feeble mind before the season starts. Team A is on the foul line, shooting 1 and 1 or shooting 2. Kid makes both free throws.
Coach "A" sends a kid to the table, who he wants to go in for the shooter. After 2nd made basket, team B quickly grabs the ball and throws it in bounds.
Is it my responsibiity, as trail to see that player, whistle to stop play, after the made basket and allow the substitute to enter?
Should the table blow the horn to get my attention, to allow the kid to come in? Or Is it the coaches responsibility to tell alert me that the player is coming in for the shooter?

Finally, why do we stop play when after Team "A" makes both baskets, they are technically not in posession of the ball, it goes to team B for the throw in. Why do we stop there inbounds effort to even allow for the substitution?

[Damian]

The ball is dead once it goes through the basket and before it is at the disposal for the other team to throw it in. During that time, the administering official (L) should blow his whistle and allow the sub to come in. The thrower still may run the base line for the throw in.

[Nevadaref]

While I agree with Damian's explanation, our mechanic here is for the TRAIL to whistle it and bring in the sub in both the 2 and 3 person systems.
The table should also give you a horn, if the player has reported before the ball becomes dead after the final free throw.

[golfdesigner]

As L I try to make one last glance to partners and table before bouncing ball to thrower, then I know if player is at table to come in, if I'm T same thing, quick look at table to see if all is okay and they are not waving frantically for some reason, then you see sub waiting to come in. If sub is at table and has reported to scorer, then I whistle as soon as ball is thru net. Then bring in sub and show in-bounder they can run baseline if needed.
Most times on spot throw-in I point to spot & tell in-bounder that they're on a spot, if they have baseline I tell them I'm starting you here, but you can run the baseline if you want to...then signal they can run..That way all know what he can and can't do..

Just my $0.02 worth.