I put zeros in after the original due date to keep everyone on the ball (you, me and parents) since assignments often overlap. Some students forget about the previous assignment and just move on.
You can still turn things in several days later for full credit because students work at widely different paces in my classes.
After a week you lose 10 points.
After that the assignment is half credit--forever. So ALWAYS go back and make assignments up even if you forgot about it before--SOME points are better than none.