So, I believe Hoid has a shard. This theory origionally came about when I noticed that when asked, Brandon would often only say that Hoid “did not have one of the 16 shards of adonalsium”. This leads me to believe that Hoid had one of three things happen to him.
Hoid carries a shard of another god.
Hoid carries some form of a dawnshard, maybe even a 5th one.
Hoid carries a 17th shard, or something like it.
So, we know from RoW that anti-investiture exists. And we also know that investiture was at one point the same thing as Adonalsium, or close to it. So I belive that anti-investiture was at one point part of another god, a sort of counterpart to adonalsium, but got shatter as a byproduct of Adonalsium shattering. The shards of this being could have been picked up by other people, including Hoid.
Another option is that hoid carries some dawnshard, or even multiple. There could be multiple instances of the main 4, or there could be a 5th one. I have less to say about this theory, as I am not well versed in the specifics of the lore surrounding dawshards.
My final idea, and the one that convinced me to make this post, is that hoid carries a shard with no intent. What I mean is that there was something, maybe a sort of sudoshard, that held the other 16 together, and gave them the sentience that was Adonalsium. When the shattering occured, this power was removed and possibly splintered. However, Hoid came into possesion of enough of this power to become a sort of vessle. Since this sudoshard didn’t have an atribute, there was no intent asociated with it. This meant that Hoid stayed unchanged, other than possibly causing his limitations, like being unable to do harm.
I realize that this post may be objectively wrong, but I made an attempt from the knowlege I had.