Cook the bacon in a Dutch oven over medium-high heat until crisp. Remove bacon from pan, reserving 1 tablespoon bacon drippings in pan; crumble bacon and set aside. Add onion to pan; cook over medium heat 2 minutes. Add green beans; cook 2 minutes. Stir in water, salt, and pepper. Bring to a boil; cover, reduce heat, and simmer 5 minutes. Stir in cabbage; cover and simmer 5 minutes. Combine sugar and vinegar, stirring until sugar dissolves. Add sugar mixture to pan; cook, uncovered, 1 minute. Sprinkle with bacon.