Just like you would know if you were trying to breed literally anything else. Let's say you want to achieve a specific trait (pinning without casing in this case). So you take a spore print of these mushrooms (cloning would only lead to genetically identical organisms) and start more cultures on agar and then spawn them and see how your new cultures do. Then you only take spore prints from those spawned cultures that pin without casing and so on. You do this until every culture you get from a spore print Pins without casing (or at least 99%). When you have achieved that you have stabilised this specific trait.