This bug happens when you try to cure a zombie villager and immediately quit the game. To reenact this situation, you just have to do the normal steps to cure a zombie villager but instead of waiting for those 5 minutes or so to finish the curing, exit the game to the menu page. Then, you enter that world again and the villager is instantly cured.
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Edit, 07.07.21:
Copied from MCPE-106839 - a new, confirmed behavior was discovered related to the bug:
Normally, a villager being cured multiple times can offer a heavier trading discount than one being cured once. However, when one save & quit the game while a villager is still being cured, upon returning to the game the villager will forget whether it has been cured before.
Steps to Reproduce:
1. Convert and cure a villager (A) multiple times, and record the trading prices. The prices would drop every time A is cured again.
2. Convert and cure A again, but save and quit the game when A is still in zombie form.
3. Return to the game. A should now be a villager.
4. Check the trading price of A. The price would be as if A is cured the first time, regardless of how many cures have been performed in step 1.
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Cleaning up old tickets: This ticket has not been updated recently (~1 year+) so is being closed as Cannot Reproduce. If you feel this is still a valid issue then please comment, or create a new ticket following the Issue Guidelines.
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This bug still occurs in 1.14.1. Probably due to game not saving the timer when exiting the world.

Bug occurs in 1.16

Affects 1.16.210.50 Beta

affects 1.16.220

Affects 1.17.0

Affects 1.17.2

Affects 1.17.11

Jay Remm: since you are the reporter on this ticket, you can and should add new affected versions yourself.

Affects 1.17.40.20