Put chicken, salt, onion, garlic, cumin, green chiles, beans, and broth in a 6-quart crockpot.

Cover immediately; cook on low 6 to 7 hours without delayed start, until chicken reaches 165°F.

Transfer to a clean plate; shred with 2 forks.

Mash 1 1/2 cups beans against crockpot wall. Add half-and-half and shredded chicken.

Cover; cook on high 10 minutes. Add lime juice; serve when broth is hot, not boiling.