In the bottom of a large slow cooker, whisk together apricot preserves and vinegar. Stir in the onion.
In a small bowl, stir together brown sugar, chili powder, salt, cumin, paprika, garlic powder, and onion powder.
Pat the pork dry with paper towels. Rub the spice mixture all over the pork and place the meat on top of the onions and preserves. Cover and cook until the pork is fall-apart tender (an internal temperature of about 205°F), about 5-6 hours on HIGH or 10-12 hours on LOW.
Turn off the slow cooker and remove the pork to a cutting board. Use two forks to shred the meat, discarding any large pieces of fat.
Stir the shredded pork into the sauce in the slow cooker. Taste and season with additional salt and pepper, if necessary. Serve on sandwich rolls with bbq sauce, if desired, or on a plate with sides.