I'm just going to describe a rules interaction as I understand it. Let me know if you see any errors in my reasoning.

When a character with attachments leaves play, the attachments are discarded simultaneously to the character being killed/discarded/etc. So the window to save the attachments is the same as the window to save the character. If I win a military challenge as the first player and my opponent chooses to kill a character with Lightbringer attached, I can kneel Ser Davos Seaworth (KLE) to save Lightbringer from being discarded and attach it to Davos. Lightbringer would still be controlled by my opponent, but it would now not be possible for my opponent to use Lightbringer to save the character that used to have Lightbringer attached. If my opponent had been first player, he could have knelt Lightbringer to save the attached character from being killed. In that case, Lightbringer would no longer be discarded by the time I had a chance to trigger Davos' ability and he could not steal Lightbringer.

schrecklich said:

Incorrect. Attachments being discarded after a character leaves play (for any reason) and becomes moribund is considered a passive (game) effect activated by that character leaving play. As such, the step/place to save attachments is separate from the step/place to save the character (although always in the same 6-Step window). For example, if a character is killed for claim and becomes moribund in Step 3, its attachments are not technically discarded (becoming moribund themselves) until Step 4. The character could be saved in Step 2, the attachments in Step 4.II.

The rest of your scenario falls apart since saving the character and saving the attachments happen in different steps

Hmmm, interesting. I was tripped up by the part in the FAQ that says that a card and all of its attachments become moribund simultaneously. I guess you have to go through the save/cancel for the attached card first before it becomes moribund (and only then are its attachments discarded). So if I want to do something tricky with attachments being discarded with the thing they are attached to, I need to find a passive ability that interacts with attachments as part of the challenge (or other event) resolution (something like "When you lose a challenge, return an attachment in play to its owner's hand"). Then as the first player I could decide which to resolve first, either the attachment being discarded with the character or this other passive effect doing something to the attachment.

I never even realized attachments also entered the moribund state. Does that mean that Venomous Blade cannot be returned to shadows after its attached character has been chosen for claim since that would be removing a moribund card from play a second time?

@Fancy B: That's correct.