Put the beans in a large casserole and cover with lightly salted water. Bring to a boil, and reduce the heat to low. Cover and cook until almost tender, 45 to 60 minutes. Drain, saving 3 cups of the cooking liquid. Return the beans to the casserole with the reserved liquid.
While the beans are cooking, in a large skillet, cook the ham fat over medium heat until it is sizzling vigorously. Brown the bacon and sausage together until the sausage is no longer pink, if using fresh sausage, or until the bacon edges are crisp, about 10 minutes.
Add the carrots, onions, and apples to the casserole with the beans and simmer over low heat for 15 minutes, covered, stirring occasionally. Add the potatoes and salt and continue to cook until the potatoes are tender, about 1 1/4 hours. Stir in the dissolved cornstarch to thicken the sauce, then stir in the butter.
Transfer the sausage and bacon and any accumulated fat to the casserole and push down into the stew. Heat for 5 minutes over low heat, covered. Then serve from the casserole. Makes 6 servings.