In large saucepot, in water to cover, bring to boil ribs and sauerkraut. Reduce heat; cover; simmer about 1 1/4 to 1 1/2 hours until meat is tender. Remove ribs. Save for another day. Remove all but 4 cups cooking liquid and 1 cup sauerkraut from saucepot; set aside.
In heavy skillet saute onions in shortening until golden. With slotted spoon remove onions and set aside. Sprinkle flour over pan drippings. Cook and stir, scraping browned bits from pan until flour is lightly browned. Gradually stir in 1 cup cold water until smooth. Stir sauce, onions, mushrooms, bay leaf, salt, caraway seed and pepper into reserved liquid and sauerkraut. Bring to boil; reduce heat; simmer 1 hour. Discard bay leaf.
NOTE: Reserved meat and sauerkraut can be prepared as follows: brush ribs with barbecue sauce; broil. Serve with remaining sauerkraut.
