Soak dried oysters in a small bowl for about 30 minutes to soften. Then rinse thoroughly to remove dirt and grit. Rinse and soak dried red dates in a separate bowl for 15 minutes. Drain.
Brush or scrape the skin (do not peel) of mature with a knife. Rinse thoroughly. Cut the cucumber into halves lengthwise. Scoop out the seeds with a spoon. Then cut into 3 or 4 pieces crosswise.
Bring 8 cups (1.9 liters) of water in a large pot to a boil. Add soaked dried oysters, red dates, prepared mature cucumber, and chicken carcass to the pot. When water comes back up 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 turn off the stove.
Serve warm in individual bowls.