Place pork, 2 cloves garlic and 1/2 of chopped onion and 2 1/2 quarts water into a pot; boil. Reduce heat and simmer until tender (about 2 hours). Strain broth, reserving pork and 6 cups of broth; discard garlic and onions.
Bring a pot of salted water to a boil. Add dried chilies and 2 pounds tomatillos; cook until soft (10 - 12 minutes).
Transfer tomatillos and chiles to a blender with remaining chopped onion, 2 cloves garlic and 1/2 cup water. Puree and set aside. DO NOT DISCARD WATER!
Return water to a boil; add purslane; cook until soft (3-5 minutes). Drain.
Brown pork in 2 tablespoons oil in a pot over medium high heat (about 4-5 minutes). Reduce heat to medium and add tomatillo puree; cook until thickened slightly (about 8-10 minutes). Transer to pot with broth. Add cooked purslane and salt to taste. Simmer until pork is falling off the bone (about 30 minutes)
