Has this actually happened to you?Yeah but they will after a few decades, granted that may not be considered "snowballing". Basically if you play long enough and don't reload battles constantly in your favor; your Kingdom and neighboring Kingdoms will be so depleted on Lords as to stand no chance against distant Kingdoms later on. Granted this would be a non-issue if they lowered the death rate - BUT that hasn't happened yet.
It's been my experience that as long as a clan reaches 18 or 19 years, the baby boom caused by game start will mean it is basically impossible to kill them off. Even the lowest of them can field their full three parties, all the time.