I saw this a few times, years ago
I met some guys who were top roping next to us in Jackson Falls, IL 25 years ago who showed us a method of retrieving your top carabiner(s) when you were done top roping.
They attached the rope to the 'biner in a strange way AND I seem to remember some para-cord being used to pull on and the 'biner would just 'unsnap' from the anchor and come down, on the rope maybe?
Does someone recognize what I'm describing?
I also recall the method as being a bit unsafe and never used it, therefore my imprecise description of the practice.