What do you mean by "engine damage"? Like broken bits dropping into the oil pan and locking up the pump, hitting the cam and gouging out a lobe, hitting the crank and punching out some cast iron? Or do you mean that if the cylinder has an intake rocker that broke, what are the consequences there, or if an exhaust rocker broke, what are the behavior characteristics?
If it's the former, yeah, debris raining down into the crankcase can kill an engine. Most of the time, it doesn't get past the cylinder head or cam valley, so it's a very slight risk. Not zero, but small.
For the latter, many of us have had this occur. On either the intake or exhaust, if you have a valve that doesn't open, you just get a dead cylinder. Like a plug misfire. It doesn't hurt anything. I once had an intake rocker fail. But my valve springs were on the weak side, so if I got the engine over 4k RPM, the cylinder would start to fire again. Vacuum was strong enough to pull the valve open enough to get some air in the hole.