Place bread crumbs into a shallow dish; pour eggs into a separate shallow dish. Heat vegetable shortening in a skillet over medium-high heat. Dip pork chops into egg, then into bread crumbs, coating both sides. Fry chops in the hot shortening until crumbs are golden brown, about 5 minutes per side. Transfer pork chops to a baking dish, leaving melted shortening in skillet.
Cook and stir sauerkraut with juice, onion, and caraway seeds in the same skillet over medium-low heat until heated through, about 5 minutes. Spread sauerkraut over pork chops and pour pan liquid over the top. Cover baking dish tightly with aluminum foil.
Bake in the preheated oven until chops are tender, 1 1/2 hour.