Place the chicken thighs in the slow cooker. Pour the salsa verde over the chicken.
Add the drained black beans, cumin, garlic powder, salt, and black pepper. Stir gently to combine everything around the chicken.
Cover and cook on low for 6 to 7 hours, until the chicken is very tender and shreds easily.
Use two forks to shred the chicken directly in the slow cooker. Stir the shredded chicken back into the salsa verde and beans until evenly coated.
Spoon the mixture over cooked rice in bowls. Top each serving with shredded cheddar cheese, chopped cilantro, and a squeeze of lime.