I can see my deleted answers. Will they ever be purged from the system, either manually or automatically? Does this kind of "deleted post cleanup" occur periodically, or will all deleted answers typically remain in the system until the end of time?
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At the moment, content posted on Stack Overflow is never deleted, except if you plead to The Team and have them exercise their SQL magic directly on the databases.
Not only can you see your own deleted posts, but all 10K+ rep users can see them as well.
So no, they're not automatically deleted in any way or at any time.