I know I read about something like this somewhere but I can't for the life of me find it, so here goes.

I was playing Obi-Wan and another character and they were both at 1 health and Obi-Wan had one die in the pool.

My opponent, playing Palpatine (who also had 1 health left) resolved the 2 shield side of his die to activate the 2 damage distributed as you wish.

I applied the first of the 2 damage to Obi-Wan's character, who lets you play a card 'Before' he is defeated.

I played Caution to remove his die and give my other character 3 shields.

We agreed that the BEFORE action interrupted the queue to play the card but we were not sure if applying the shields happened before the remaining damage reached the second character.

Thanks! (Flame away)

You couldn't trigger Obi's ability and save other character that way. Here are the rules:

When a player distributes damage “as they wish:”
1. The player assigns their characters the amount of damage
they will be dealt.
A player cannot assign an amount of damage greater
than the remaining health plus the number of shields on the
character, unless a player cannot assign any more damage
to their characters and there is still damage remaining to be
assigned, then the player must assign the remaining damage
to their characters as they choose.
2. Once all damage is assigned, it is dealt simultaneously.
Example: A player has two characters with 1 remaining
health each. They are forced to distribute 2 damage from the
special on the F-11D Rifle (r8). They must deal each of their
characters 1 damage, instead of dealing one of the characters
2 damage. If one of those characters had 1 shield, then both of
the damage could have been dealt to that character.

Due to the damage being dealt simultaneously it wouldn't help. Now if you were able to play a card that would kill Palp Before Obi is defeated, you would win the game. I think there is some hunker down ruling or something that covers this.