DoN (Destruction) cannot target a card that is not in play for its discard, nor the ability on any card not in play for its negate. The default is "in-play" for both, so DoN has to target an artifact that is still in play; by the time 4DC completes (which must happen before a dominant can be played), it is out of play and cannot be targeted by DoN. Similarly, a "negate and discard" that does not specify out of play does not work with a card that is already out of play, because it is not in the area of default targeting.
There are exceptions to both, however, where the cards can be targeted that are out of play. You could use one of the new CoW cards
Paying Taxes or
Treasures of War against 4DC; since they both refer to "last artifact" they can 'reach' anywhere that artifact ended up, so long as it was the last one. If your opponent uses
U+T and then activates another artifact, you still can't hit U+T with this (it wouldn't be "last" in that case), but whatever the last one to activate can be targeted even if it leaves play or goes face-down in artifact pile. Similarly, a card that says "negate and discard last," like
Sign of the Rainbow, can 'reach' anywhere that target went, because it has a specific target that overrides the normal default targeting.
Lastly, anything that causes Special Initiative can be targeted anywhere by any card that can target its type:
When a player is controlling character(s) in battle and an opponent's special ability, or a game rule that has been triggered by an opponent's special ability, would leave that player with no character in battle when the special ability has completed, they have Special Initiative.
When this occurs, all abilities are paused and suspended (including additional abilities on cards played or any triggers) and the player with their character(s) being removed has the opportunity to play an Enhancement that will interrupt or negate the ability that is causing the removal (or that triggered the corresponding game rule). The enhancement played must be able to interrupt or negate the removing ability. If the card with the removing ability was already removed from play due to its ability, it may still be targeted during Special Initiative by an enhancement that specifically targets its card type.
