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People also get fired from jobs for not doing their jobs on a daily basis even if no one writes in big red letters DROP DEAD DEADLINE on the job requirements. How fast would a secretary be fired for saving up all the faxes to be sent on Friday because faxing is a pain? Pretty fast, in my experience.
I have worked with that secretary, and the powers that be chose to educate her rather than fire her. She's still there and actually does a great job now (or did the last time I was there).
I also have scaffolded assignments, and I also have students make excuse after excuse only to be told, "sorry you can't do the speech because you haven't done assignments X,Y,Z." I have also had students (trad and non trad) who couldn't get it together the first couple of weeks but took their lumps and went on to finish the semester well - and felt like heroes for bouncing back and conquering their work.
As you point out we still have no idea what is in that syllabus, or whether the student is leaving out key elements of the story.
But as an educator I take issue with cutting off the opportunity altogether. Someone upthread said "the P in PhD doesn't stand for psychic." While funny, and meant to remind the student to communicate with the instructor, I think it's also fair to point that statement in the other direction and say that despite years of experience and a good instinct as to how this situation will play out, there are always outliers, and we're not psychic.
When this happens in my online courses I tell the student in question, "based on missing assignments X and Y you now need to get __% on all the other course material to get a C, __% to get a B and 110% to get an A. You can drop now and get a partial refund or continue on and take your chances. What do you want to do?" Most students drop, a few soldier on and pull their B/C. I've never had a student earn lower than a C after that message (although I've only been teaching online for seven years - I guess there's still time!). However, they take on the responsibility for the situation, and I'm not blamed for kicking them out before they had a chance to improve, as is happening here.