Preheat the oven to 400°F.
Place rye bread cubes in a 9" x13" casserole dish and place in the oven to toast the bread (approximately 10 minutes. Toss after 5 minutes).
Remove bread cubes from the casserole dish and set aside.
Spray the casserole dish with cooking spray. Spray one sheet of aluminum foil with cooking spray.
Spread the sauerkraut over the bottom of the casserole dish. Top with corned beef strips and dressing. Top with bread cubes and cover with the foil sheet, sprayed side down.
Bake for 20 minutes. Remove foil and sprinkle Swiss cheese over the casserole. Bake an additional 10 minutes or until cheese is melted and bubbly.