Canvas does have a feature available from the Canvas Gradebook called the "Message Students Who" feature, which allows you to send an Inbox message to any students who have not yet completed a particular assignment. How do I send a message to students from the Gradebook?
With that being said, this is not an automatic process, as it does require the instructor to initiate the send. Since there is not an existing related Canvas Feature Ideas, you might consider creating a new request in Ideas. (How do I create a new idea conversation in the Instructure Community?)
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