Ideally, they would also alert you that you've been "marked as dead" and give you a week or so to claim that you're still around.

They do exactly this. There are several layers of checks because getting it wrong is kind of a deal-breaker.

A lot of things happen after confirming someone is really truly dead, and many of those things can't be easily undone :)

(Full disclosure: I work for the company that developed the site)