Many people complain that their posts are suddenly deleted without warning and without a note.
While some content can be eliminated to improve the site's overall quality, it seems rude not to inform the author that his contribution is gone.
So how can information on MiYodea be deleted without informing the author?
To answer the question in your title, yes, content can be deleted without informing the author. This happens frequently with comments and occasionally with posts.
The help center explains why some answers are deleted. Answers can be deleted a few different ways:
When an answer is deleted from review, fairly often one of the reviewers will check off one of the boilerplate review comments. That comment tells the author that the post is in review and might be deleted, but there's no further notification if it is.
When an answer is deleted by the community or a moderator, somebody might or might not leave a comment. I can't speak for anybody else, but I try to leave a comment if I think it would do some good -- for example, letting a new user know that new questions can't be posted as answers, or suggesting fixes that the author could make to get it undeleted. If I'm deleting a post for reasons that have already been covered in existing comments, I usually don't see the need to add a "yeah, what they said" comment.
If a post is deleted by red flags (spam and rude/abusive), there's no comment and the post is locked. Unless somebody commented before deletion, there won't be any notification -- but also, the vast majority of such deletions are from new, unregistered accounts that have not contributed anything positive to the site.
If the question is deleted, answers get deleted as part of that and usually there are no comments. I've occasionally commented on an answer that was a victim of question deletion that I think could be repurposed elsewhere, but usually that doesn't come up or I don't notice the deletion in time. (Moderators can always leave comments, but they'll only ping the user if posted within an hour of the deletion.)
People have asked on Meta.SE for notifications for deletions, and SE has always declined them. You can see any of your deleted posts if you have the URL, which you might from a past notification or your browser history. You can see your recent deleted posts from your profile (there's a link at the bottom of your questions list and your answers list). And if you have 10k rep, you can see all of your own deleted posts by searching for user:me deleted:yes.
