Set the roast on a large plate or platter, and cut off any excess fat.
Drizzle olive oil on both sides of the pork. Using a pastry or basting brush, spread the olive oil evenly on the pork.
Sprinkle the dry rub evenly on all sides of the meat so that the roast is completely coated.
Transfer the meat into the middle of the slow cooker pot fat side-up. Top with any excess dry rub that's left on the plate.
Cover with the lid and cook on the low setting for 6 hours.
After the roast is done cooking, transfer the pork to a large serving plate.
Using tongs and a fork, (or 2 forks), pull the pork apart in opposite directions to get long and fairly thick shreds (or thin shreds if preferred). Ladle some of the liquid that is left in the slow cooker on top of the meat.
Do a taste test and add salt if needed.
Serve while warm. This pulled pork makes a wonderful meal served as is, topped with fresh lime juice along with rice and black or pinto beans. And leftovers make delicious sandwiches and soft or crispy tacos.