Let's suppose a question was deleted by the Community. What's going on with that question? Can this be undeleted by the OP? How long does it stay on M.SE, that is, after how much time is it totally removed?
Deletion on Stack Exchange is almost entirely soft deletion, meaning that the content still exists, but it just hidden from most users. While some data can be hard deleted, this requires intervention by SE employees, and is very rarely done. Even the most vile of offensive trolling posts still remain in the database. Cases where this might happen is if a user unintentionally leaves personal information (SSN, credit card information, etc.) in a post (and then usually just a specific revision of the post is deleted for good).
Most of the information about deleted posts can be found in the Meta Stack Exchange deletion faq. A few important points.
- Users can only unilaterally undelete their own posts if they were the one to delete it. (There is one other eventuality in which a user can unilaterally undelete their own post, and that is if the post was deleted from the review queues by mostly "recommend delete" votes, as opposed to "delete" votes. It is pretty rare for posts to be deleted from the review queues on math.SE.)
- Posts deleted by moderators (including SE employees) can only be undeleted by moderators.
- It used to be that posts deleted by Community were considered the same as above (Community does have a diamond after all), but this was recently changed. Now posts deleted by Community are treated as posts deleted by sufficiently-privileged users, meaning that they require 3 "undelete" votes by 10K users.