THEY ARE THE SPREN OF PARSHMEN LONG DEAD. THEY ARE THEIR KINGS, THEIR LIGHTEYES, THEIR VALIANT SOLDIERS FROM LONG, LONG AGO. THE PROCESS IS NOT EASY ON THEM. SOME OF THESE SPREN ARE MERE FORCES NOW, ANIMALISTIC, FRAGMENTS OF MINDS GIVEN POWER BY ODIUM. OTHERS ARE MORE ... AWAKE. EACH REBIRTH FURTHER INJURES THEIR MINDS.
THEY ARE REBORN USING THE BODIES OF PARSHMEN TO BECOME THE FUSED.
The Fused are the souls of those who refused to move on. Essentially, they're using the innate vulnerability within the Parsh species to form a connection, thereby pinning each their souls to a new vessel.
This is why they can't be killed in any permanent sense, because it would take a great deal more power than any non-Shard has access to in order to harm them.
Further, they are ancient singers who survived their deaths and are able to possess living singers during form bonding in the Everstorm. They are the highest authority in the singer society. They have powers similar to Surgebinding.
Hoid has mentioned one of the names of a Fused, which sounds like they knew each other, so either there's something more, or the Fused have been around a much longer than readers have been told. That Hoid would have been friendly with some of them implies that he knew them before the first Desolation.
(To be continued.)
Because their minds and self identities have been so corrupted by repeated deaths and trauma, they now have tarnished mental images of themselves. So, when they each inhabit a new host, each their identities corrupts it fully, thereby creating strange, almost bestial creatures of themselves.