If a project is an assignment and public in a space it should be visible to all other space members. There is a space filter on the right hand side of the space which could interfere with this. If the student has set the filter to "Yours" they would not end up seeing a public assignment owned by another user in the space,
It is possible for a student to delete their copy of an assignment. This would result in the student's copy disappearing and moving to the trash but should not impact the students ability to access the original assignment.
If this doesn't resolve the issue if you could send the space, project, and user experiencing the issue to us we could investigate a bit more on our end.