I have a minor theory that I have thought after noticing a few things.
- Throughout the succession arc, we are constantly reminded about post mortem nen, more so that we ever have until now. Combined with how constant death is in this arc, this leads me to believe that it will be used very prominently by major characters in other ways that we havent seen yet.
The sun and the moon is shown and explicitely stated to overwrite conditions for other abilities disappearence, and in more than one way: we see it remain in Chrollo's book first, and then we see it mantain the gallery fake clones. And this is explained as a consequence of its previous owner's will. Chrollo himself says that stolen abilities sometimes evolve and change limitations
- The fact that Chrollo and Kurapika have a lot of parallels is not exactly a hot take, but at this point it feels like it could be an excellent moment to capitalize on it narratively. Plus they are both showing rampant death flags, although Kurapika looks more ambivalent about it (especially regarding Woble).
Chrollo also says one thing: that the "next best options is already in place" and "the spider will live on" after his death.
The idea is: if Chrollo were to die, between his determination to protect the spider and Sun and Moon previous lingering will, what would happen to Skill Hunter? Could it persist aftert death as post mortem Nen?
As a conjured item, the book itself could just mantain itself of course and potentyially go to the next leader of the troupe. But it would still require a user, and since we know that Specialization is not exactly easily accessible I am not inclined to believe that the ability would be simply passed along with possesion.
But we know of another character that has conditional, Specialization based ability-stealing that is channeled through a Conjured object, don't we?
That's right, it's Leol Kurapika!
Let's think about it for a moment. Kurapika has slowly been moving from seeking revenge (by killing the Troupe), to seeking solace(by finding the eyes), to end up fulfilling the only thing that he truly wanted: to protect. Which perfectly aligns with the wish of the Meteor City elder. Plus, what better way for Kurapika to show that he has moved past his hatred than accept the "help" and will of the Troupe past leader?
So if :
Kurapika took Skill Hunter through Steal Chain
Chrollo died in the meantime
Skill Hunter would still be inside Steal Dolphin, and potentially not disappear after use due to Sun and Moon.
Plus, it could easily merge with the condition for steal dolphin, which just so happens to be the one for Kurapika's Specialist state: only being usable during Emperor Time.
Did I cook? Am I insane? Let me know!