It's not infrequent, especially nowadays, given that people are still travelling well into old age! Before hip and knee replacements, small disability scooters etc, most people would have given up travel altogether by the time they reached their octogenarian years!
I don't know what the current procedures are, but under Dan-Air, my wife was always told to make the body look like a passenger in a deep sleep in his/her seat and draw a blanket up to the chin. I believe BA tries to accommodate the body in one of the toilets (but how you're supposed to drag a deadweight corpse to a toilet without attracting attention beats me!)
It's a very sad situation for all concerned, made worse by the bureacracy and red tape involved.