Some context: I was intrigued by a short discussion in another answer relating to dealing with late submissions of work by students, where Jeff suggested giving students a limited number of 12-hour "late tokens" that they can use at their discretion when submitting work late during a course. The idea of this is to give each student a "budget" for lateness, so that mild sporadic lateness would be okay, but repeated or extreme lateness would break the budget. This seems like a very clever idea to me. Hence, the purpose of this question is to solicit information on any other unusual/innovative practices lecturers use to deal with late submissions of assessment in their courses.
Question: What kinds of unusual/innovative methods do lecturers use to deal with late submission of assessment?