Can't be done as far as I know - and even if you could, what is the point? If you can extract a file from a zip archive, the user is then free to delete or copy that file at will, as with any other file.
If it is the zip archive you want to protect, the user can always create a new archive and delete your one, defeating any measure you take - if anybody would want to that is.
Please be aware that trying to prevent people from deleting files is going to end up with your product being treated as malicious - a potential virus, in effect.
-Stewart