Combine the pork, onion, garlic, 1/2 cup water, 1 teaspoon salt and a few grinds of pepper in a 6- to 8-quart slow cooker. Cover and cook on low, 7 hours.
Remove the pork and garlic from the slow cooker to a bowl using a slotted spoon. Strain the juices, discarding the onion; transfer 3/4 cup of the juices to a small saucepan. Add the ketchup, mustard, brown sugar, pickle brine and hot sauce. Cook over medium-high heat, stirring occasionally, until the sauce is just starting to simmer and thicken, about 5 minutes.
Heat the vegetable oil in a large skillet (preferably cast-iron) over high heat. Add the pork and garlic; shred the meat with two forks. Cook, stirring occasionally, until the pork is crisp and golden, about 5 minutes. Season with salt and pepper.
Toast the bread. Top with the pork, sauce and coleslaw. Serve with the pickles.