Sprinkle dry rub mixture on top of roast, making sure all sides are well coated.
Pour applesauce and vinegar in bottom of crock pot making sure it is well mixed.
Place roast in pot and cover with remaining onions.
Pour water into crock pot so it is just about covering the roast. You should be able to just see the top of the roast above the water.
Cook on low for 6-7 hours.
Pull pork from pot when it is tender enough to shred with a fork. Using a strainer, drain the liquid from the pot, reserving the broth for later. Take the strained onions from the colander and place back into crock pot. (You can use a brand new onion for this part, but I like a very tender onion so I reuse the original).
Shred pork with a couple of forks or your hands and return to crock pot.
Pour barbecue sauce over meat and mix thoroughly. Use some of the reserved broth to help mix sauce in thoroughly and to help keep the meat moist during the last part of cooking.
Turn the crock pot on high for the remainder of cooking, leaving it for at least another hour so the meat can soak up the barbecue flavor. (Keep the reserved broth nearby in case you need to add more during the last stage of cooking).