For me, homework (rare), and written assignments have strict due dates. I don't generally accept them late unless a student is absent on their due date, but they also have a low impact on grades, about 10% for me. Tests and quizzes are a non-issue because they are generally due at the end of the period. They make up a larger portion of the grade. I don't often allow for extra credit on these, but maybe an extra credit question at the end.
Projects however are a different matter. Projects make up a large portion of the grade; it's what we spend the most time doing. I have deadlines for projects, and I grade all projects on the day of the deadline. I make sure that my deadline is reasonable. If a large portion of the class is not yet done, then the deadline was unrealistic, and I'll adjust it a bit. If there are just a few stragglers, it may be that they were too chatty and unfocused, and the deadline was reasonable. From time to time I'll have a student behind because of a few days of illness or vacation, and I'll handle those a bit differently or alter their assignment so they can meet the deadline.
When a project is done and the deadline is reasonable, I grade all projects on that due date. I grade in class and usually assign written work on that day to keep students occupied, or maybe sketching for the next project so I can grade. Students complete a rubric, I review it, and make adjustments if necessary, and record the grade.
If a student has 50% of their work complete, I grade it as a 50 out of 100. They know they can work on it more, but on their own time. I will even allow them to sign out supplies. I do not hound them for their project, I let them know it is their responsibility to get it in. When it's done, or has been improved, I change the grade without penalty. However, when the marking period ends, all grades are permanent. I'll warn students about that date, and remind them that any make-up work must be done by then.
This is beneficial in a few ways. I do not have to hound students. Their parents can see the 50% and the comment I left, and they hound their child. It instills a bit of personal responsibility on the student.
I also send emails home when work is late or missing because that kind of issue should be documented so no one is surprised if a grade is low or a student fails.