In a slow cooker, combine onion, chicken, tomatoes, enchilada sauce, beans, corn, broth, chili powder, cumin, and garlic powder. Cook on High for 3 hours, until chicken is tender and an instant-read thermometer inserted into thickest part registers 165°.
Transfer chicken to a cutting board or plate and shred with 2 forks. Return to slow cooker and stir in cheese and cream. Cook on Low until cheese is melted, about 5 minutes; season with salt, if needed.
Divide soup among bowls. Top with sour cream, cilantro, a squeeze of lime, crushed chips, and more cheddar, as desired.
