Even if the dog was somehow able to magically perform a half-gainer with a 360 and end up getting into messing gear teeth, you STILL have the clutch pulled in. You hear or feel the transmission gernading itself, so you keep the clutch pulled in until you come to a stop. Or, you start to release the clutch and you feel or hear the transmission gernading itself, so pull the clutch back in all the way, apply the brakes, and come to a stop.
Opposing scenarios are welcome.
Well that's all well and good IF the dog doesn't get caught someplace "down stream" of the clutch but I believe you will find that the clutch is in between the crankshaft and the transmission not between the transmission and the output shaft. So if something jambs up the transmission gears holding in on the clutch will have no effect on the locked up transmission and the rear wheel connection!
As for expecting the broken part to just sit in the bottom of the transmission and play nice. I wouldn't make any bets on it. With all those gears spinning around throwing oil every which way in a vibrating engine not a chance I would be risking, especially not for someone else!