A friend of mine found the remains of a good-sized duck in his cellar wood stove when he went to light it in the fall.
Another friend found several dead bluebirds
in her greenhouse heating stove. The heater had a simple stove pipe chimney with a metal cap. Apparently they liked the gap that ran all the way around the pipe just below the cap, but when they hopped in they couldn't get out again. I tried making a bluebird house based on the same principle of a 360-degree entry slot below an overhanging roof, but it didn't attract any birds at all, just a family of mice the next winter.