I hunt with the barrel clean and free of oil. No fouling in the bore, and no caps or primers fired. I leave the gun loaded until I shoot it, unless I hunt in the rain.
If I shoot the gun and reload to begin tracking or to continue hunting, I always clear that load before the next day's hunt. Even if it's not raining, that fouling will absorb moisture from the air, which cannot help anything.
I generally don't fire the gun to clear it. I'll either pull the bullet in a sidelock, or push it through in an in-line. I can re-use my FPBs that have been pushed through.