When a user tries to acces a deleted question, if they don't have 10k+ reputation or diamond moderator privileges, they'll only see a generic message like "this post has been deleted for reasons of moderation". This is even true if the user is the owner of that question.
For answers, there are mechanisms in place to ensure that user will get notifications for moderator comments even if their answere is deleted. This is important to be able to explain to the users what they did wrong, and still be able to delete the post right away without having to wait for the user to come back and read the feedback. I've made a feature request to extend this beyond just diamond moderators to all moderating users, but that still only works for answers, not for questions.
I don't want to let crap questions stay around longer than they have to, I'd like to just vote to delete them right away. But if I vote to delete a question right after closing it (especially on the sites where I'm a moderator), the user might not have visited the question in the meantime. In that case he won't receive the feedback that hopefully was given in comments, and he also won't be able to even read the close reason.
So what I have to actually do for crappy questions is to close them, and then remember to check back after a while to delete them, when I think the user has read the feedback. This approach has several drawbacks, it lets the crap stay visible on the site for longer, and it forces me to memorize or note the post so that I can revisit it.
I shouldn't have to do any of this to ensure that the user receives his feedback, the only considerations for deleting should be the quality or lack therof of the actual post. As a diamond moderator I also have to make sure that I don't prevent the community from moderating by deleting borderline questions too quickly.
Users don't need to be able to see their deleted posts forever or have the complete list of those in their profile, but they should be able to see them for a short time after they're deleted if they haven't seen all comments or the close reason yet. The post should stay visible for them, listed in their profile and notifications on it visible in the global inbox until they visited the deleted post, or a specific timeframe like 48h after deletion.