I just finished writing a really long answer, and damn am I long-winded, ugh... so here is the short version: It is true that "then" clauses don't resolve if the first part of the card doesn't resolve.
But does "then" resolve if the first part of the card is PARTIALLY resolved? I dunno. My thoughts are expanded below...
sorry if I wasn't clear... At first we were talking about "then," and that's when CJ quoted the FAQ. Now I'm talking about whether or not the first part of the card is considered to be "resolved" if the effect isn't fully resolved. The more I think about it, the more I am inclined to answer Mndela's original question as "yes."
what I'm trying to say is:
An effect can be resolved successfully and have no impact on the game state. You can deal 0 damage, or add 0 threat, and still successfully have resolved an effect.
But some cards direct you to do something specific: discard 3 cards, or deal 2 damage, or whatever. If you can't do that, maybe the effect doesn't resolve successfully.
So here are examples of text that (I think) could do NOTHING, and then you would still be able to resolve a subsequent "Then" clause:
-Search the encounter deck. Add any enemies found to the staging area. Then, xxx...
-Discard all attachments. Then, xxx...
-Give all players each taco in your refrigerator. Then, xxx...
-Search your sock drawer for any number of black socks, and put all progress tokens inside them. Then, xxx...
-Draw all copies of the Ace of Spades from your deck. Then, xxx...
In all of those fake examples (did you know they were fake?!), I used non-specific language: "all, any, each." Those concepts include "0." So you can resolve the effect even if you don't have any tacos, or black socks... you get the point.
But a card like Ered Nimrais Prospector uses specific language: discard 3 cards. If you can't do that, the effect isn't fully resolved, and the "then" clause wouldn't activate. Still, I could be wrong, because there is this thing in the FAQ:
"Q: If I can’t discard 3 resources from all of my heroes
due to Bitter Wind (KD 56), do I have to partially fulfill
A: Yes, players should resolve as much of any
“discard” effect as they are able to."
So if you play Ered Nimrais Prospector, you can partially fulfill the effect by discarding 1 or 2 cards. Or even 0, I guess. But does that count as "successful resolution" and allow the "Then" part to activate? The more I type about this, the more I think "yes it does" (contrary to my original answer). But I'm not sure... thoughts?