Place the roast and onion in a 3 1/2 to 4 quart slow cooker. Pour in the beer. Add the soy sauce, paprika, salt, and pepper. Cover and cook on low for about 6 hours, or until fork tender. Time will vary by slow cooker.
Transfer the meat to a cutting board. Using two forks, pull the meat apart into shreds, discarding any fat. Strain the onions, reserving 1 cup of the liquid. Return the shredded pork, onions, and reserved liquid to the slow cooker. Serve or make BBQ sandwiches.
For BBQ Sandwiches:
Stir in the barbecue sauce. Cover and cook on low for 15 minutes, or until heated through.
Serve on sandwiches between buns with toppings of your choice.