They're most likely deal with it on case-by-case basis.
If their death "look" normal enough then they'll just make sure nobody can connect it with the skip.
If the death doesn't look normal but very few people (such as police officer) are aware of it, they'll use cover up story and memory wipe those few witnesses.
If the death doesn't look normal and many are aware of it, they'll use cover up story, memory wipe key witnesses, and discredit who/whatever spread the news to the point that anyone mentioned it will be laughing stock.
Body double is likely the least used option. Why bother? People meet untimely death is pretty normal. Unexpected, but not really out of ordinary. Not to mention that the double has to deal with all of the dead person's acquaintances, which is much harder to fool than public (although amnestic help). Even if they really have to do it, I think it'll last only as soon as the Foundation can arrange their disappearance from public.