I just tried to visit the profile of an MSO user, but it turns out that that user recently deleted his account, so I got the "Page Not Found" page. It looked like this:
The "log out" and "tools" links were missing from the top bar. I know the site knows who I am because I've been logged in all day with no issues and the badges/privileges banners are still there.
The same behavior occurs on questions that don't exist, except that I don't always see the badges/privileges banners on those.