The ones who retire due to skill just hang out in your barns afterwards. They can't show but don't demand any payment either anymore and give you time to reassign their horses. The 65 ones however retire on RO as they age up on the 1st like the horses do and if you haven't yeeted them before that they will just abandon your horses and have you scurrying through the barns to figure out which horses (and how many) they are - I hate that!!!
Just checked, it's called skill, not level, sorry for the confusion. So basically if a level 9 rider gets to 900 skill points they will usually retire the next day (hit level 10)
They also retire after hitting level 900 in a discipline, which is why I'm very cautious with riders level 890+ currently have one at 899 - that one's getting the boot before next payment day!