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Combine 1 tablespoon sugar, paprika, bouillon and pepper in small bowl. Press rub onto all sides of pork.
Heat oil in large skillet over medium-high heat. Brown pork on all sides until deep brown. Place pork in 5- to 6-quart slow cooker.
Add water, ½ cup vinegar, onion, tomato sauce and remaining 3 tablespoons sugar. Cover; cook on low for 8 hours or high for 5 to 6 hours. Meat should be fork tender and shred easily. While pork is cooking, prepare coleslaw.
Combine cabbage and carrot in medium bowl. Stir in remaining ¼ cup vinegar and dressing. Cover and refrigerate.
Shred meat with 2 forks.
Place liquid from cooker in large skillet. Boil for about 10 minutes. Should be reduced somewhat.
Stir 1 ½ cups liquid into shredded meat. Serve on buns with coleslaw and pickles.