In a two-block high house (meaning the ceiling is the third block up, with two empty blocks under it), a carpet makes a villager too tall to walk around. If there is a carpet in front of a door on the outside (like a doormat), the villagers can't get in. If there's a carpet on the block just inside of a door, the villagers stop in the door's space and can't go further. Villagers used to be able to walk on carpet, but I think one of the updates made them a tiny bit taller. Now when I go to one of my old villages, I find all the villagers who happened to be standing on a carpet in a house trapped in place. Until I destroy the carpet they're standing on, they can't move at all, and unless I destroy the carpets around them to give them a path, they can't go anywhere.