1. Trim excess fat from pork roast. Sprinkle with salt. Place in slow cooker and pour vinegar over roast. Cover and cook on low until roast is fork-tender and pulls apart easily, 8 to 10 hours.
2. Remove roast from cooker and shred meat into small pieces. Discard cooking liquid. Return pork to slow cooker and stir in barbecue sauce. Continue to cook until warmed through, about 30 minutes.
3. Spoon coleslaw onto bottom half of hamburger buns. Layer with pork, then top with the other half of the bun. Serve immediately with extra barbecue sauce on the side.