Does a bear shite in the woods?
If it is a common brown bear, or grizzly, it will often defecate somewhere other than the woods, as their area ranges over a vast array of topography, including rivers, marshland, and grassy plains. Polar bears may find some scrub trees or bushes at the edge of their tundra range, but definitely not what would be considered officially a forest. So polar bears do not expel feces in the woods. However, the most commonly found bear species in the lower 48 states, the black bear, has primarily a forested range. His bowel movements are the most likely be completed in the woods.
And contrary to popular folklore, a rabbit's feces are hardened pellets because of its lack of dietary variety, therefore the fecal matter is expelled cleanly from the anus without contact to its rectal fur, however, a bears feces would indeed become matted and entangled in a rabbit's coat if said bear were to use a rabbit to clean its anus after a bowel movement.