[MC-159300] Villagers that have been infected by a zombie can despawn, even if they have been traded with

The bug

Villagers that have been infected by a zombie can despawn, even if they have been traded with. This makes it very difficult to rescue villagers after they have been infected, as the player may not move further than 128 blocks away from the infected zombie villager to gather all supplies needed to cure it. This might be intended.

To reproduce

Set difficulty to hard
Spawn a villager
Trade with the villager
Spawn a zombie
Let the zombie infect and convert the villager
Run /tp @s ~ ~255 ~
→ The zombie villager despawned