In a large saucepan, combine water, juice of one lime, thyme sprig, peppercorns, garlic powder, onion powder and salt. Bring mixture to a boil. Add pork chops, reduce heat to medium-low and simmer for 1 to 1 1/2 hours, until meat is very tender. Add more water as necessary to keep chops covered.
Turn off heat and let the chops rest in the broth for 30 minutes. Remove chops from broth and shred, removing excess fat; set aside.
In a large frying pan, heat olive oil over medium-high heat. Add the shredded pork and fry until it is almost crisp, about 5 minutes. Add the onion and garlic and continue to cook until the onion is just tender yet slightly crisp, about 10 minutes more. Add the juice of one lime, mix though and toss with cilantro. Serve and enjoy.