Any investigator may defeat the enemy with Smite the Wicked attached to return Smite the Wicked to Zoey's discard pile.
If Zoey is eliminated (by being defeated or taking a resign action) while Smite the Wicked is in play, Smite the Wicked's Forced effect triggers, as per the FAQ [V1.0, section 'Rulebook errata', topic "Elimination"].
If you draw Smite the Wicked and discard cards off the top of the encounter deck until the deck is empty without drawing an enemy, you do not reshuffle the encounter deck: "Generally, you reshuffle the encounter discard pile into the encounter deck when it is empty, but not while you’re resolving an effect. So you would discard cards from the top of the encounter deck, and if you happened to run out, then you’re in luck: Smite the Wicked fails to resolve, and is discarded. Then you reshuffle the encounter deck & discard pile."
- If you draw Smite the Wicked and the enemy found has a spawn instruction: "Smite the Wicked overrides the enemy’s normal spawn location. So if you draw Smite the Wicked and the enemy that you find is a Swamp Leech, and the farthest location happens to be a non-Bayou location, the Swamp Leech would spawn there and immediately get discarded, along with Smite the Wicked."
Revelation - Discard cards from the top of the encounter deck until an enemy is discarded. Attach Smite the Wicked to that enemy and spawn it at the location farthest from you.
Forced - When the game ends, if attached enemy is in play: You suffer 1 mental trauma.
One of those signature Weakness that can end the Campaign. Looking at the two elements, the effect and the discard condition, we get:
The effect: The nasty sting is that if Zoey is taken out by damage or horror, she ends up with 2 Trauma for her troubles. If you are unlucky enough to have this happen a couple of times, it's new investigator time. Fortunately, unlike Searching for Izzie, this card asks you to do what Zoey always wants to do.
The discard condition: Well, you discard it when the enemy gets killed, which is exactly what Zoey wants to do. It can be extremely variable, since you can draw a Swarm of Rats or a Servant of the Lurker. Drawing an Aloof enemy is, of course, extra annoying. It also benefits from the "loophole" that anyone can resolve it, so if a very weak enemy comes out or another investigator is combat-ready, this can be dealt with pretty easily. As usual with this style of Weakness, when you draw it is critical, as is the map. Drawing it one turn before Resigning or dooming out in The Unspeakable Oath is way worse than drawing it early in The Secret Name. It can take anywhere from 2 to 6+ actions to clear, so it is a very situational weakness. You can mitigate the effects with "Get over here!" or Righteous Hunt.
All in all, this is an above average signature weakness, maybe a bit above average.