Revelations from Patch 5.3

[Vyrerus]

Haurchefant came back

While it's true that seemingly the souls of Haurchefant and Ysayle came back to help the WoL and Alphinaud(not Aymeric, he was a witness not a participant) pull the eyes out of Estinien, that's something I chock up to the writers wanting a symmetrical capstone moment, rather than adhering strictly to the in world soul lore, which is already wishy-washy at best. Up to that point we're already shown that despite our first blade of aether not killing Lahabrea, merely banishing him from his host body, that we could use something very much like it to straight up kill an Ascian, and we do kill one when we, with the aid of Moenbryda, kill Nabriales.

The reason Ser Zephirin uses a javelin of light in his attempt to kill the WoL, which Haurchefant thwarts, is to put us down, since the WoL is effectively immortal unless their body is completely destroyed due to The Echo. I guess we could say the writers have never 100% decided whether or not it means soul death, but I'd always considered the Ascian soul destruction context to mean that when blades of light are in play, souls die.

You need a huge amount of aether to pull off killing the soul.

Yeah, and it's been a theme of every MSQ except for Stormblood's. In ARR it's gathering the Crystals of Light, and then later using an aetheric siphon/Tupsimati to do the same thing. In Heavensward it's done again with an eye of Nidhogg. Twice. The sheer amount of aether is never actually specified, and in the earlier showings a sunder Ascian took the same method as an unsundered one, though Lahabrea's soul was directly absorbed into Thordan. For Emet-selch we got a stakes raised version of what's been the case several times before, with yet another completely different happenstance for the death of his soul, being he had a hole punched through it, rather than total oblivion/absorption. Ser Zephirin throws a javelin of pure aether, and it kills Haurchefant, body and soul. Him showing up in the Nidhogg death scene is fan service, imo.

Ascians are immortal because they've already "died".

This is not the case. Ascians are immortal because that is a trait of beings who have perfected control over The Echo. See Zenos, the Sahagin Elder, the WoDs in HW, and even the player controlled WoL. They only need Crystals of Darkness(or Light) to retreat to the rift, or another body to possess, prior to the Blessing of Light being sealed, as demonstrated by Nabriales. It's one of those old plot points that was hastily done away with, and sort of never referenced ever again.

As for a line of dialogue that tells us that their souls are destroyed, it comes from Urianger, the second time the scions convene after defeating Iceheart as Shiva. The line is, "'Tis our belief that an Ascian soul may be permanently undone if smitten by a sufficiently concentrated burst of pure aether."

As for Elidibus

The Exarch first hit him with that huge wave of aether, eroding his soul down to its constituent aether, which is then absorbed by the tower. He is permanently gone, because his soul was undone first, and then absorbed, much like Lahabrea.