I don't know if this will be helpful or not...it doesn't look exactly like what I've experienced...but close.
What I have seen that looked a bit like this involved use of third party plugins...my agency also uses the Face-to-Face module to allow students to register/book themselves for sessions (or teachers to register/book them). When the teacher registers/books students, the module displays all potential students in the site, including those who are not enrolled in the course, for possible registration/booking. If they register/book a non-enrolled student, it adds them to the enrollments area (manual enrollment) but without a role. If you un-register/book them, it leaves them on the enrolled users with no role. It is very strange. (I think the original F2F language is booking, but I've replaced it with registration in my language pack.)
Then, because the students don't have a role, sometimes you can't find them on the add/remove enrollments list. To get rid of them, you have to assign them a role and then remove them from manual enrollments. The thing that is different is that my enrolled users displays the enrollment type at the right corner and yours appears to have some sort of icon/image. It may be my theme displays differently than yours.