I see a few questions on this but no answers that helped, so I put this together to potentially help out others here.
If you have the “Students can only participate in the course between these dates" box checked, it will cause the course to remain in the Courses list and on the Dashboard forever.
This is one of those quirks of Canvas. If this box is checked, the course will show up in student’s Courses list, even on the Dashboard forever. Even if the term has ended, they’ll continue to see this course.
I should also note that this box seems to get checked automatically when you are copying an older course forward, so that may be the reason we see it happening so often.
This issue has caused a steady stream of tickets to our support. Hopefully this advice helps out your organization.