.. before the damage itself can be assigned, say from something on the shadow card like 2 damage to every wounded character or whatever, does that mean the attack is then undefended and you must assign the damage to a single hero? Or is the attack considered resolved as the shadow effect goes into play?

Core set rulebook. Page 18. Last paragraph.

It becomes undefended. This is one of the ways the game punishes chump blocking.

So if the shadow effect is deal 1 damage and that kills the defender, would the shadow effect then upgrade to the undefended attack 2 damage? Or is the shadow effect considered executed at that point, but the attack itself still has to resolve, which is now considered undefended so all the damage has to go on one hero.

The shadow effect is resolved so you won't deal more damage for that effect. But you still have to resolve the attack itself, so yes the damage from the attack would be considered undefended and you'd have to place all of it on a hero.

Also, the shadow effect would have language like "deal 1 damage to defending character." If the attack is undefended in the first place (i.e. if you never declared a defender), that shadow effect would do nothing, as there is no defending character.