So, because of the void/abyss ambiance and particles in the throne room of the Pale King, the fact that all kingsmoulds are drained of their void in that room, and the generic darkness of it, it is clear that the Pale King's end was heavily related to void. But what was the exact end he met?

 After all, the Pale King was a Pale being, and the void is not but a liquid, which acts like a typical fluid, unless a will is imprinted on it. 

So you may ask: Did some random Pale King hater find a way to imprint their will to the void and kill him? 

Well no, I personally believe that the will imprinted into the void that ended the legacy of the Pale King, was not but his own. 

Void is typically said to be in relation with regrets.

Now it's pretty easy to understand what the Pale King had to regret: Murdering millions (possibly billions but that's not the point) of his children in his attempt to save his crumpling kingdom, and keep Hallownest eternal, and after failing, running away and hiding, leaving the kingdom to die on its own.

The fact that this is what killed the Pale King, is cryptically supported through his dream nail dialogue, that reads: "No cost too great...", "..." possibly implying that he tried to make himself think that what he did was worth it, and then dying of depression, when he realised what he had done was pointless, and all things come to an end.

So, yeah, this is in my opinion the fate of the Pale King. If you want, comment what you think of this theory/speculation.

I have figured out the Pale King's fate (Kinda speculative)