1.Mostly TG in adipose tissues are used to generate all ATP needed
2. Some urea is still generated and bear has to get rid of this urea- but not via urine and the bear cannot metabolize urea directly.
3. Urea enters the GI tract and bacteria secrete urease which splits to Nh4+ and HCO3-. Bacteria then convert that ammonium to non essential and essential amino acids. And then they are re synthesized to bear's needs.
4. Small rate at which the bear catabolizes proteins is matched by the synthesis of new proteins via the bacteria in the GI tract.
For more details read:
Clinical Detective Stories- By Mitch Halperin, MD and below