Prepare the Pork:

Mix brown sugar, paprika, salt, black pepper, garlic powder, onion powder, and cayenne pepper in a small bowl. Rub this spice mixture all over the pork shoulder.
Place the pork in a slow cooker. Add apple cider vinegar and water around the pork, not over it to avoid washing off the spices.

Cook the Pork:

Cover and cook on low for 8-10 hours or on high for 4-5 hours, until the pork is very tender and shreds easily with a fork.

Shred the Pork:

Remove the pork from the slow cooker and shred it using two forks. Discard any excess fat or gristle.
Skim the fat from the cooking liquid and return the shredded pork to the slow cooker. Add barbecue sauce and mix well. Keep warm until serving.

Assemble the Sliders:

Split the slider buns and toast them lightly if desired.
Pile a generous amount of pulled pork on the bottom half of each bun. Top with coleslaw if using, then cap with the top half of the bun.

Serve:

Serve the sliders warm, with additional barbecue sauce on the side.