When a parrot is tied to a fence with a leash, it stays there. But when any player loads the chunk the parrot is in, the leash might break, freeing the parrot and teleporting it to the player if he/she is close enough. Sometimes it just makes the lead invisible, but the parrot is still tied to the fence and the fence still shows the lead around it.

This doesn't always happen when the chunk gets reloaded, but it does happen some times.

To recreate:

• Tame parrot
• Leash parrot to fence
• Leave chunk, let chunk unload and reload chunk again

The reloading of the chunk can be done by the player itself or other players.
If the server has unloaded the chunks because of no player activity, this can also be done be reloading the chunk by loggin in.

Tested only on 17w13b multiplayer server. Couldn't replicate on singleplayer.