Hi Sharders!
Long time lurker here but this is my very first post.
Forgive me if this has been discussed but I don't think I have seen it yet though with all the ideas thrown around on this forum it is hard to keep track sometimes.
I am of the opinion that the Fused are in fact souls of dead Knight Radiants who have been broken or corrupted by Odium.
As far as I have been able to tell no where in Oathbringer does it actually say that they are Parshendi (it does say "they" and "their" though). From memory it says they are ancient soul of leaders and kings who are valiant warriors from long ago. From what we know of the cultures on Roshar, that sounds a lot more like KR than parsh.
I believe that this would explain their access to Voidbinding too, as well as their deteriorating minds.
As quite a few people have speculated, due to the Nahel bond replicating Honorblades, perhaps an unexpected side effect was that they get sent to Braise, like the heralds, after death. With the link to their spren broken at death this would leave their cognitive shadow stuck on Braise without hope of resurrection, giving Odium an unlimited amount of time to break their minds. Also with the Nahel bond broken, Odium would be able to easily fill the cracks in their sDNA with the requirements for Voidbinding. I think the KR learned this from Honor when he was losing his mind which was the final straw that caused the Recreance.
Lastly, to back to back up this theory is the fact that all of the Fused eyes are permanently Red, indicating corruption by another shard.
My other theory, along the same lines is that the Fused are the souls of the original Voidbringers, the first humans to settle on Roshar. This would be a better explanation for Voidbinding as they would have arrived on Roshar with it after destroying Ashyn.
I do enjoy reading theories that get shot down as much as the plausible ones so if I am completely off the mark please let me know!