As I understand it, the due date can be set and Late Submissions can be set to no - what happens then is that the student can submit their assignment after the due date, but it appears in red as they do so, flagging up that it was a late submission. Otherwise Late Submissions can be prevented . . . in which case the option to browse for and submit the file disappears on the due date.
Assignment
"Prevent Late Submissions" option in 1.9
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