When you have e.g. a renamed pig and it gets struck by lightning, it gets turned into a Pigman which still got the name of the pig, but its PersistenceRequired tag which was set to 1b by renaming is gone (= 0b), which results in despawning of this mob.
The same goes for e.g. a Villager turning into a Witch, the Witch will keep the Villagers' name, but will despawn/her PersistenceRequired tag will not be set automatically to 1b.
Now, at least with upcoming raids in Minecraft 1.14, and with the possibility that a previously Villager who gut turned into a Villager Zombie and then cured again to a Villager retains his old trades, this seems to be a logical conclusion that a "turned" mob should stay persistent, also considering that they keep the nametag-name after all.
This is not a suggestion, but I consider this a bug, however, it is completely up to Mojang to decide whether or not this is not a bug, but WaI.
Sorry if I overlooked a bugpost for this issue, I looked around and couldn't find it, which I find puzzling, as I'm quite sure that it must have been mentioned already, but probably there are again no tags in the bugpost, or none with which I could find them.