Bring water in a large pot to a boil.
Add chicken carcass, red dates, and winter melon to the pot. Cover and bring water back to a boil. Reduce heat to low. Simmer for about 1½ to 2 hours. Skim off any scum appearing on the surface.
Season with salt and add goji berries. Continue to boil for another 5 minutes. Turn off stove.
Serve warm in individual bowls.