Yes, I've had my TB mare for 6 years and her previous owner emails me every year on her birthday to see how she is. I send her an update and recent photos.
No way for two of my horses - one is a total nutter and weirdo, the other likes her horses so fat they border on laminitis and IMHO shouldn't be keeping any.
My other horse's old owner is part of the YO family and is great!