Place the pork shoulder into the ceramic bowl of a slow cooker. Pour enough water and white vinegar into the slow cooker to assure the pork is completely covered, maintaining a 2-to-1 ratio of vinegar to water. Add the salt. Put the ceramic bowl in the refrigerator and allow the pork to marinate at least 12 hours and up to 24 hours.
Drain enough of the liquid from the ceramic bowl until about 1/2-inch of pork is left exposed. Add the onion to the remaining liquid. Season the exposed surface of the pork with the cumin, mustard, chili powder, and brown sugar. Place the bowl into the base of the slow cooker and cook on High until the pork is tender and falls apart easily, 8 to 10 hours.
Carefully remove the pork to a cutting board; shred the meat into strands using a pair of forks. Remove and discard any excess fat.