I slightly confused about something. Regarding supporting a player, the core rules state: "Stealth, if applicable, must be declared against characters controlled by the player who is the original target of the attack.".

I don't understand why this verbiage is in there. If you can only support a player in a challenge if they do not declare defenders, but stealth can only be declared against the original target's characters, why wouldn't they just say stealth cannot be re-declared? If the challenge went undefended then there aren't any characters controlled by the original target in the challenge to declare stealth against anyways.

Maybe because when a player redirects a MIL challenge against themselves with Lord Commander of the Kingsguard title, you are actually allowed to redeclare stealth as the attacker against his characters. That is the only instance I am aware of where stealth can be redeclared.

The verbiage you just quoted appears to be incorrect for the above case.

Bomb said:

Right, but in the above case, if the new target of the redirected attack decides to go undefended, and his supporter defends for him, stealth still cannot be declared against the supporter. So the same question remains. In your case above, stealth can be re-declared against the new defender, but not against the new defenders supporter.

Two reasons it is written the way it is (other than the fact the Lord Commander title, a true redirect, works differently from "supports," which is not considered a redirect at all ):

1. Your reasoning that Stealth is declared just the one time, while completely true, is not necessarily obvious or intuitive to everyone. They see the declaration of "support" defenders as a new and different defense action, which might allow the attacker to use Stealth a second time on the "new" defender. By wording the entry the way it is, it is made clear not only that Stealth is declared once, but that declaring "support" defenders is considered part of the original "declare defenders" framework action.
2. The entry also makes clear that the "support" rules do not create some sort of exception to the Stealth rules. Otherwise, people might (and almost certainly would) decide they could declare stealth against the characters of a supporting player, as a potential defender, when they originally assign stealth.

Ok cool, i just wanted to make sure that I was understanding it correctly and that there wasn't some other situation/circumstance that I was missing.

I must've misinterpreted the FAQ entry on Lord Commander, I didn't realize Stealth could be declared after that redirect. Learn something new everyday.