@agnirm ,
Chris may not have used it himself, but he's correct. This is the way it works.
Changing the availability does not wipe out the results. Canvas makes it difficult to remove any student submission. The only place I've found (I haven't tested everything) where student work may be lost is in a discussion when you allow editing. In that case, only the final copy is kept. Also, if you delete a student post, there is no easy way for the instructor or even the local Canvas admin to recover that post. Chat and external tools may act differently, but for assignments and quizzes made within Canvas, every submission is available to the teacher.
When you change the availability for a single student, it renames the others as "everyone else" and leaves them as they were.
The resubmit button will appear as long as current date is in the availability interval, which it will be for the one student but not "everyone else." Canvas allows resubmitting assignments and leaves it up to the instructor to decide what to do with it.
Quizzes work differently than assignments. There students are also limited by the number of attempts and possibly time limits. But for regular assignments, this is exactly what you want to do when you want to allow the student to make up the work.
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