Broil the tomatillos and poblanos 4 inches from the heat for 8 to 10 minutes until blistered, then blend them with the onion, garlic and broth.
Season the pork with the salt, heat the oil in a skillet over medium-high heat, and brown the pork in 2 batches for 5 minutes per batch.
Transfer the pork to a 6-quart crockpot, add the cumin and green sauce, and cover immediately.
Cook on low for 7 to 8 hours until the pork reaches at least 145°F and pulls apart easily with a fork.
Stir in the lime juice and cook uncovered on high for 15 minutes if the sauce needs to thicken.