More complex summary

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.

How to reproduce bug

Setup:

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.

Note:

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.

Expected result: 

The door does not change at all seeing as the villager is far away from it.

Actual Result:

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.

Attachments

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.