The Chronicle has an interesting article on late work, "What it her Grandmother Really DID Die?" by Christopher Hirschler, http://chronicle.com/article/What-If-Her-Grandmother-Really/127927/
The comments are interesting as well.
His solution was to adopt one of the insights of distance learning:
Rather than saying it is OK to miss a class, for example, professors can adopt strategies of distance learning and independent study to provide alternative assignments that are rigorous and enable students to acquire the requisite knowledge. Such options might be more challenging than the missed class or assignment, thus providing a disincentive to miss class without legitimate, if unexplained, reasons.
Dropped assignments, projects with multiple due dates, built-in "extra" assignments... all of these strategies enable you to maximize student learning while minimizing the need to assess the relative validity of the variety of student excuses. This can be critical because sometimes the issue causing a student to be late with an assignment isn't something we would deem important or life-threatening. It's just the last in a long list of problems and happened to be the one that caused their house of cards to collapse. Tonight the student skipped your class because their child had a soccer game. But they didn't get the assignment completed early because their mother was having cancer treatments. You might have no sympathy for the soccer game, but that might be the excuse you hear.
Flexible assignments mean the more private students don't have to talk to you about the challenges in their lives. Online we do hear a lot about our students' lives, but that doesn't mean some of them still aren't living their lives outside of class. Privacy is a gift we can give to our students.
Here's an interesting attendance policy from an anonymous poster in the comments area:
Students who are regular attendees 'earn' one 'sick' day per month which they can accumulate and use any way they see fit, including for funerals, though not for cutting out at the last minute on presentations and exams. They simply let me know before class starts (however they can leave a message) that they are taking their 'sick' day. I promise that I will never ask them why they will be absent because, as I say on the first day of class, I want to support their thoughtful making of prudential judgments about multiple goods, i.e., being in class or doing something else. This is a sobering thought for many of them. Treating them as responsible adult decision-makers makes a big difference in attendance rates.
I wish my daughter's high school teachers would try that one!
Life happens -- consider building flexibility into your courses in areas where that is possible. And where you can't.... well, that is similar to real life also. Sometimes the deadline is hard. Sometimes there are multiple ways to meet a learning outcome.