Bring the liquid to a boil, stir in the rice, cover with a tight-fitting lid, reduce the heat to low and simmer until the water is absorbed, about 20 minutes.
Bring the water to a boil, reduce the heat to low and simmer covered until the rye berries are cooked and the water has been absorbed, about 40 minutes.
Bring just to a boil; reduce heat to low, and cook at a bare simmer, adding water as needed during cooking to maintain level of liquid until stock is flavorful, about 2 hours.