First I’m going to reflect on what Haki is. Of course it is a power in the world of One Piece, but more than that it is a manifestation of Willpower.
The direct translation seems to be a combination of Willpower, Ambition, and Fighting Spirit. I will just use Willpower to refer to this combination of traits. As is true in many Shonen, willpower or ambition allows characters to achieve supernatural feats. I believe every supernatural feat in One Piece can be attributed to Haki, from Zoro lifting a building in Alabasta to Luffy surviving copious amounts of poison in Impel Down. We know these happened due to the character’s immense willpower, and that their willpower is inseparable from their Haki. They are one and the same, in the One Piece world Willpower itself manifests as supernatural abilities.
The main distinction is when Haki is referred to directly by the characters it is representative of a conscious effort to use Haki, as seen in Observation, Armament, and Conqueror’s Haki. This conscious form of Haki is most similar to the trope of Ki that is ever present in Shonen, however I do not think it is separate from Willpower but just a conscious manifestation and specific utilization of it.
However, even these conscious forms of Haki do not actually require consciousness!
Here, Luffy’s Fighting Spirit and Conqueror’s Haki are both on display while he is unconscious. This is because they are not separate qualities! They are intimately linked.
One does not even need to be in their own body to use Haki, as it comes from the spirit.
Here, Sanji in Nami’s body is still able to use his Observation Haki. Haki comes from one’s spirit, not one’s physical body.
So what am I getting at?
Willpower is a common theme in One Piece, not just in terms of personal feats but in terms of Inherited Will. Of course the Will of D is maybe the biggest example of this in the story, but Inherited Will pops up in many character’s personal arcs. Chopper has inherited Dr. Hiruluks will, and more relevant to the current plot, a bunch of Samurai have inherited the will of someone very powerful.
So here is my theory:
Oden was a man of such incredible Will and such incredible Haki (because they are inseparable qualities) that his Haki did not die with him! When Kaido questions if the Scabbards have Oden’s Ryou, which we know is what Wano calls Armament Haki, he is not saying they happen to conveniently have the same ability as Oden. He is questioning if they have actually inherited his Haki! In the One Piece world if Haki is inseparable from Willpower, then it follows that Haki does not die with one’s physical body. Oden says his soul will live, and it did! The Scabbards are being strengthened by the disembodied Willpower Oden has left behind, and this is what lets them pierce Kaido.
I believe this is being set up to be revealed by Oda because it has huge implications of what the Will of D really means. Roger’s Willpower was so strong it set into motion the Great Age of Piracy. Joy Boy’s Haki has been waiting for the right person to come along and inherit his Will! This is why Luffy is the new Joy Boy, not because of some divine destiny, but because he is the individual worthy of inheriting the Will.
*Theory by isasweetpotato