Heat oven to 325°F. Put corned beef and water in a snug Dutch oven; bring to a simmer on stove. Cover; braise 3 1/2 to 4 hours until meat pulls apart easily, rotating once to submerge the exposed surface.
Drain beef; cool enough to handle. Shred into short pieces, removing large fat pieces. Increase oven to 350°F.
Mix mayonnaise, ketchup, relish, and Worcestershire into thick dressing. Split connected rolls horizontally; put bottom slab in a parchment-lined 9-by-13-inch pan.
Spread dressing thinly over bread. Layer half the Swiss, drained shredded beef, dry sauerkraut, and remaining Swiss. Replace top slab.
Mix butter and caraway; brush over rolls. Cover with foil; bake 15 minutes. Uncover; bake 8 to 10 minutes until center reaches 165°F.
Rest 5 minutes; cut into 12 generously filled sliders.