No question is too dumb to ask at least once.
Really? OK, I'm convinced. I've decided to play it really safe when my vintage doubles need to have their barrels cleaned, and fly in a Purdey Trained Barrel Smith from London to take care of them. No better, safer way to do it!
Actually, I have managed to do general cleaning of all my shotgun barrels by holding them in my left hand and brushing or swabbing them out. I don't have the muzzles resting on a pile of patches in the bottom of any padded bucket either. The muzzles are clear of the ground so the bristles of the brush can clear, and any excess solvent can drip out onto a section of newspaper on the basement floor. All of the dirty patches also end up on the newspaper, and the mess gets taken out and burned when I'm done. I have always managed to do this without ever once dropping or otherwise damaging my barrels. Of course, if I am going beyond a simple cleaning where the use of a cleaning rod chucked into a drill is required, a vise with padded jaws will be used, and the end of the barrels will be supported as well. I don't want 28 or 30 inches of barrels hanging out there unsupported, clamped only by the lumps at the breech end. Since the rod I use in my drill is made of aluminum and is therefore much softer than the steel of the barrels, I am not at all concerned about damaging either chambers or chokes. I am not allowing my rod to become impregnated with abrasive particles. I would resort to a bushing if I was going to be in there a while cleaning up pits with abrasive paper or a hone, for example. Now, If I was cleaning a rifle, I would be much more concerned about cleaning rod damage to throat or muzzle lands. I even use a ramrod guide to load my flintlock rifles except while actually hunting.
This is all common sense... very basic common sense. If I want some penetrating solvent to remain in my barrels, I orient them horizontally. If I want solvent to drain out, I turn them vertical so gravity can do it's thing. There absolutely are questions too stupid to ask. The question posed in the subject of this thread might be OK if it were posed by a rank beginner. But it's not. And anyone who is so uncoordinated as to drop their barrels while swabbing them is just as likely to damage them by dropping them on to, or out of, their barrel vise. Anyone that careless probably shouldn't handle loaded guns.