Adjust oven rack to lowest position and heat oven to 250 degrees.
In a small bowl, mix sugar, paprika, garlic powder, pepper and salt to make a dry rub.
Line a shallow pan with foil. Pat the pork roast dry. Place it on a rack set over the pan. Lightly sprinkle the top and sides of the meat with additional salt, brush with half the mustard, then sprinkle with half the dry rub. Carefully turn roast over. Repeat the process with a little extra salt and the remaining mustard and dry rub.
Place pork in oven and roast until a meat thermometer registers 170 degrees (about 9 hours, depending on roast size).
Remove pork from oven. Let sit until cook enough to handle. Meanwhile scrape drippings into small saucepan, add 1 cup water and bring to simmer.
Cut pork into 1- to 2-inch chunks. In a large bowl, pull meat apart with fingers into bite-size shreds. Add the pork liquid and optional barbecue sauce and stir.
Can be covered and refrigerated up to 3 days. When ready to serve, warm in the microwave or in a covered pot over low heat.