The messages left behind by the last generation of Knights Radiant hinted that when Melishi, the only Bondsmith of that generation, imprisoned the Unmade Ba-Ado-Mishram in a gem, parts of the Parshendi's souls were ripped away, creating the dullform Parshmen. Later when the Everstorm arrives, we see the missing parts of their souls restored or replaced and the dullform Parshmen regaining their identities.
When Kaladin and friends are on the Honorspren ship, Notum mentions that swearing the 5th set of ideals involves the merging of souls between the spren and the Radiant. I'm guessing that the process of "killing" a spren and making it a deadeye was analogous to that of the Parshendi and dullform. Breaking the oaths may cause the human and spren souls to be forcibly ripped from each other, rendering the spren into a lesser state of being.
If deadeye spren are the result of spren missing parts of their souls, I wonder if these could similarly be restored and the deadeye spren brought back to life.