Place the chicken in the slow cooker and pour the jar of chunky salsa evenly over the top.
Cover and cook on low for 4–5 hours (about 240–300 minutes) or until the chicken is cooked through and tender.
Remove the chicken and shred it with two forks, a hand mixer, or a stand mixer; return the shredded chicken to the slow cooker.
Add the can of refried beans and 1–2 cups shredded cheddar cheese to the cooker, stirring to combine.
Cook on low for at least 30 minutes more, until the beans are heated through and the cheese is melted and creamy.
Serve the cheesy bean salsa chicken in warm tortillas and add a dollop of sour cream if desired.
Instant Pot option: add chicken and salsa to the pot, seal, and cook on high pressure for 20 minutes; allow pressure to release, shred the chicken, drain most liquid, add refried beans and cheese, and use Sauté for a few minutes until cheese melts.