Cut the pork tenderloin crosswise into three pieces. Add the pork, tomatillo salsa, chicken broth and 1 teaspoon of salt to the slow cooker and cook on LOW for 6 hours.
Preheat oven to 400 degrees.
Place all the peppers, onion and garlic on a sheet pan lined with parchment paper. Drizzle with 1 tablespoon of olive oil.
Roast the peppers, onion and garlic until browned and softened, about 30 minutes. Allow to cool. Remove the skin from the peppers and discard. Squeeze the roasted garlic cloves from the papery skin and discard.
Add the roasted peppers, onion, garlic cloves, cilantro, lime juice, remaining 1/2 teaspoon of salt and remaining 2 tablespoons of olive oil to a food processor or high powered blender. Blend until smooth.
Remove the lid from the slow cooker and shred the pork. Stir the green sauce and the drained beans into the chili. Cover and allow to cook on low for 30 - 60 additional minutes.
Taste and add more salt if necessary. Serve the chili topped with chopped red onion, cilantro and sour cream.