Can a character with a duplicate be killed twice if one death occured during a player action window and the second would occur because of military claim or another player action window during the very same challnge?

Well, a character cannot be killed twice. That's because once it goes Moribund you cannot make him leave play for any other reason.

However, when you save a character from being killed he doesn't die. You saved him, right? He wasn't killed. They can try to kill him a second time, only this time you might not be able to save him.

A save doesn't bring a character back from the moribund state - it prevents him from going moribund in the first place. A character targeted by a kill ability will become moribund in step 3 of the action window only if you fail to save the character or cancel the kill effect in step 2. So if you have a character with a dupe that you saved from a kill effect or claim by discarding the dupe, the character was never killed and was never even moribund. If a second kill effect goes off in a subsequent window, the character can be targeted again. If you can't save him or caneel the effect this time, he will become moribund and then die at the end of the window.

Edit: Apparently I didn't see the two previous posts that beat me to it.

There's an important distinction - you can never "kill" the same character twice, but you can choose him to die for an effect then save him. If your questions refer to a saved character being chosen again for a separate effect, the answer is yes. As long as the effects are separate effects. If a card effect would kill 2+ characters, they cannot both be the same character, and if a game effect (eg; claim) would kill 2+ characters, they cannot, once again, be the same.

However Die By the Sword or No Quarter can kill the same character as was chosen for claim or from the other effect, provided he's not moribund at the time they are played (as previously mentioned).

So chars don't go into moribund unless every attempt to save them failed?

Correct. Characters do not become moribund if they are successfully saved. Further, moribund cards are removed at the end of the action window in which they became moribund. People have a tendency to over-apply moribund. But when an action window closes, player or framework, all moribund cards are removed from the table. The state is THAT temporary. So moribund will only ever factor into Response and passive effects.

It's worth noting that "moribund" does not enter into the answer for the question originally asked.

In the original question, the deaths are taking place in two different action windows, so moribund is not a factor. Either the character dies in the first window (a player action window in the OP) and is gone for the second, or the character did not die, so gets to the second action window (settling claim in the OP) in the normal, not moribund, state.

So don't confuse yourself with moribund on the original question. The answer there is simply "if a card is saved from one effect (with a dupe or anything else), it is fair game for a second, new effect; this is true even if those 2 separate effects both take place in the same challenge."

Or no attemp is made at all. Correct.

MrFixit said:

Cards enter moribund state when an effect that would remove them from play sucessfully resolves. Saves are one option that allows you to interrupt such an effect and thus prevent it from resolving sucessfully.

In other words, a cards goes moribund if
A) an effect that would remove it from play works on them (i.e. they are targeted by such an effect or affected by an untargeted effect) AND
B) that effect isn't canceled AND
C) they are not saved from that effect.