My parents are leaving their front door ajar so home helpers and nurses can come in. Dad is very slow moving and worries about not getting to door in time for deliveries or visitors. I am concerned for their safety as well. I would love to hear how others have solved similar issues. Thank you!
I'm interpreting your question as he is leaving the door somewhat open. If you can show him that there's ways to keep the door shut and locked until someone comes (like suggested in the other responses) and they can let themselves in and out.
But if he doesn't remember this solution, then maybe install a home security alarm system that alerts YOU that the door is not closed and calling him to shut it? Or is there a neighbor in proximity who you can enlist to go over to shut it for him?
It has been wonderful and is exactly like the ones real estate people use. You can find at Lowe's, Home Depot, etc.
You can change the code occasionally if needed.
Very easy to manage. Can also be used for food deliveries.