A friend once had a squirrel get between the chimney and the liner and rattle around for a while. It could never get out, so he built a fire hoping to kill it. It died, but despite being very well cooked, it still managed to stink abominably for a while.
I live in an apartment with a hood over the stove. In the last few years, I have had numerous problems with birds getting into the ventilation duct, resulting in bird crap, feathers, twigs, straw, and the occasional dead bird in the in the grill over the stove and on the stove itself. I've repeatedly complained to the landlord, who claims to have put screens over the vents. After my fourth or fifth hazmat operation, cleaning everything with bleach, I just gave up and recently wrapped the grill with tin foil to keep stuff off of the stove. It still stinks from time to time. I of course can no longer do any cooking beyond boiling water for tea, since there's no ventilation. All of my "cooking" is now confined to the microwave.