In the past I could trap a zombie villager and save him to cure him later. This works because they do not normally despawn.
The Bug:
Zombie villagers now despawn and cannot be saved for later due to this.
To Reproduce:
Trap a naturally spawned zombie villager, go do other things and he will not be there when you come back.
All hostile mobs can despawn. A hostile mob can only be prevented from despawning by being named.
See also MC-159298.