When villagers are obstructed by multiple doors, they will keep opening a door, no-matter how far they are (unless out of simulation distance). Also, they will stop when killed, but only after the body despawns.
Initially, create a setup where there are two zombies standing alone a few blocks away from each other (make sure there is a block above their heads). Next, go a block or two away from the zombie and make a three wide platform of solid blocks, repeat for both sides (make sure they are facing inward). After that, create a bridge of glass between the platforms. Finally, place doors on every glass block including one of the edges of a solid one. For help with this setup look at the images provided.
Make sure this is high up to prevent villagers path-finding to the ground.
Step One: Summon or spawn a villager on the solid block with the door on.
Step Two: If the villager gets stuck opening the door ahead of it, simply teleport is to a cage a few blocks away. If the villager acts as normal, hit it away from the doors and teleport it into a cage.
The door does not change at all seeing as the villager is far away from it.
You will see it keeps opening, try to close it and you will see you can't. Also, you will constantly hear the door opening sound.
I have attached the necessary screenshots and a testing world for this bug in the hope that someone might send me a video I can include in the attachments.