Place the sauerkraut, caraway seeds, brown sugar, and apple into a large saucepan over medium-low heat, and bring the mixture to a simmer. Reduce heat to low, and cook for 2 hours, stirring occasionally.
Preheat oven to 325 degrees F (165 degrees C). Grease a 9x13-inch baking dish.
Place the bacon and onion into a skillet over medium heat, and cook until the bacon is almost crisp and the onion is beginning to brown, about 10 minutes. Stir the bacon mixture into the sauerkraut. In the same skillet, brown the kielbasa sausage in the remaining bacon grease until the sausage begins to brown, 10 to 15 minutes; stir into the sauerkraut mixture. Spoon the sauerkraut and sausage mixture into the prepared baking dish.
Bake in the preheated oven until bubbling, about 1 hour.
