Hello @irefrixs!
If the 3 threat is not part of the cost, shouldn't that threat still be removed even if the deck runs out? As the only thing after the arrow is additional threat.
I tested some scenarios with 2 cards left in my deck and got this.
Discard 1 (aspect) -> 4 threat was removed
Discard 2 (aspect and neutral) -> 4 threat was removed
Discard 3+ -> No threat was removed.
But I agree, strictly RAW it's unclear as the cost arrow is mandatory.