Why did I read this post today?
I put a brined bunny in the slow cooker this morning. Red potato, onion, carrot, celery, mushroom soup, bacon fat, beef stock....I put considerable prep work into this potential masterpiece and aticipated a nice stew when I got home from work. Just your reminder of pierced paunch and bladder stench will likely put me off my feed. You may well have unwittingly made my dog's day.
In Michigan we would head shoot them with .22's late in the season when they were the only open game. The few rabbits I now bag are incidental game, unluckly to cross my path when I'm after birds, and therefore killed with shotguns. Occasionally one gets minced, but no more so than birds. I do think cleaning mammals is several degrees nastier than birds, regardless of how they met their end.
To answer your question: It happens. Most are okay. If one stinks of inner liquids like you describe (ugh the thought), I toss it. Are you saying the shotgun minced the rabbits or the beagles had some raw nibbles? Heavy loads?
At least two of my friends are not the least bit agreeable to shooting rabbits and squirrels in the presence of their bird dogs. I guess they don't want their dogs to diverting attention and energy to rabbits or looking up trees?
