1986 trans am, 305 TPI, 4spd auto. So the car will stall if I stop suddenly, and it seems worse after longer drives. I can stop very very gradually and avoid this, but if I'm driving and come to a complete stop, the RPMs will drop to like 400-500 and sometimes stall out. If I stop very gradually the RPMs will slowly rise back to its normal idle around 750-800RPM. (Idle air control valve opening?)

Anyone know why this happens?

 

It might be a sticky IAC valve, or the IAC passage is clogged and needs to be cleaned out. Perhaps the IAC is closing when you're in motion (the car's momentum will keep the engine running), but then isn't able to react quickly enough when you come to a stop.

Try unplugging the lockup TCC connector from the transmission. That will prevent it from locking the torque converter. If that helps, then it implies the TCC solenoid might not be unlocking properly.
Another possible cause is if the ECM doesn't know the car's speed (and so it doesn't know when it should be signaling the TCC to unlock). But I don't know if it's possible for that to be the case if your speedometer is still working.

Do you have any Check Engine codes? (Make sure the bulb is working - it should come on during the key-on bulb test)
Did you have the car before this problem started, or is it an issue you've inherited and don't know the history of?
Has the ECM been swapped or messed with? I've had an issue like this before when I messed around with settings on a modified chip, but it wouldn't be applicable to the stock chip.

 

Had this exact issue it ended up being the pole piece in the distributor was a little rusty - worked fine until hard braking then the g force of the stop would alter the air gap just enough to stall. Once standing still it would start right up every time.