Pat the pork shoulder dry with paper towels. Rub evenly with Hawaiian sea salt and drizzle the liquid smoke over the entire surface of the pork.
Place the pork into a slow cooker or Dutch oven. Pour the water around the pork and cover tightly.
Cook on LOW for 10–12 hours in a slow cooker or at 300°F for 5–6 hours in the oven until the pork is fork-tender.
Remove the pork from the cooking vessel and shred it using two forks. Reserve the cooking juices.
Add the chopped cabbage to the slow cooker or pot with some of the reserved cooking juices.
Cover and cook for 20–30 minutes until the cabbage becomes tender but still holds its shape.
Return the shredded pork to the pot and toss gently with the cooked cabbage.
Cook for an additional 5–10 minutes so the flavors combine, then serve warm.