You may allow your students to submit their assignments even after the due date has passed.
This article will help you to set up your assignments including setting due dates.
Once you add a due date to your assignment, you have the option to Allow students to submit this assignment after the due date has passed by clicking into the box to the left of the text.
Once you click the box, you have the option to put a limit to how late the student can submit the assignment. Click into to the date box to enter a date and time.
Now you can enter a penalty that will be applied to the assignment if it is submitted after the due date. This penalty will be entered as a point value. Note: The total point value associated with the assignment is located just below the penalty points.
You will know if a student submits the assignment after the due date, because the date and time of submission will be in red.
Click into Grade Assignments and choose the Assignments tab
If you want, you may manually apply a penalty to any assignment that was submitted late.
Click on the student's name to see the actual assignment submitted by that student.
Scroll to the bottom of the assignment. Change the grade to whatever you want (notice that the grade is not a percentage). Click into the boxes next to Send notification to student and/or Flag to alert student and write an optional message to explain to the student why the grade was changed.
Be sure to click the Submit button.
If you decide that you do NOT want to allow anymore assignments to be submitted, you may choose to uncheck the box next to Allow students to submit the assignment after the due date has passed within the settings mentioned above.
To learn more about grading assignments, read this article.