2013-07-01 : If the permanent is still a legal target but is not destroyed (perhaps because it regenerated or has indestructible), its controller still gets the Beast token.

2021-03-19 : If the target permanent is an illegal target by the time Beast Within tries to resolve, the spell won't resolve. No player creates a Beast token. If the target is legal but not destroyed (most likely because it has indestructible), its controller does create a Beast token.