I think two clarifications would help here. First, the bug that makes villagers vanish has to do with time, not location. If any of your villagers die and are buried or decompose, you are at risk (usually low risk - the bug doesn't happen to most people) of them vanishing if you grab them and drag them somewhere, regardless of where they are in the village. If you exit the game after burials and then launch it again, you shouldn't run into that bug.

The second is that doctors won't heal a villager who is "Weakened." Their status has to actually show that they are "Sick" in order to be healed (and they will usually be coughing if you pick them up). You should always check a villager's details screen before you try to heal them to make sure that they're really sick (unless you want unexpected babies).