Final answer:
Bears lose mass during their winter sleep by metabolizing their fat stores to maintain vital functions, turning it into energy, carbon dioxide, and water.
Step-by-step explanation:
When bears emerge from their dens in spring having lost a significant amount of body weight, the mass is essentially 'lost' through metabolic processes.
Throughout the winter during their deep sleep, bears still maintain near-normal body processes and body temperatures, meaning they continue to burn calories to sustain vital functions, which is why they are not in a true state of hibernation.
They use up their stored fat, which they accumulated during the warmer months from eating plenty of food, to generate heat and to fuel their metabolism. This stored fat is converted into energy, carbon dioxide, and water, which they exhale or lose through waste. This is how bears ‘lose’ the mass during their long winter rest.