Can a stallion be "over" bred

I'm just curious about this as it's foaling season on social media so I'm starting to see this a lot coming across my fyp. Seeing some stallions being chosen over and over again, one I read is going to be nearing over 800 foals, and remembering people talking during the Kentucky derby that every horse on the track was a descendant of Secretariat. It had me wondering if there is a point where a single stallion can be bred far too much that it actually becomes detrimental to the breed instead of the other way around.

Just a curious non horse person.