Quick answer
Dropboxes allow draft submissions by default. They can simply submit their work to the dropbox.

Full answer
Students can keep submitting drafts up until the deadline. Each new submission overwrites the previous draft. When the due date is reached, a Turnitin dropbox simply processes the most recent draft submitted by the student. 

Do bear in mind that once a student has submitted several drafts, Turnitin slows down the processing time. After 3 draft submissions to the same dropbox, it takes 24hrs or more to return a Turnitin report. It’s worth reminding students at this point that the aim of Turnitin is not to get 0%. For more information, please see this handout, produced by Faculty staff, explaining how students and staff can interpret a Turnitin report: https://docs.google.com/document/d/1lXRnSlXVggwwq7upkTrcrrEV6jPXZBGu/edit?rtpof=true