Place the chicken breasts in the slow cooker.
Add salsa, ground cumin, chili powder, corn, black beans, and low-sodium chicken broth to the slow cooker and stir to combine around the chicken.
Cover and cook on low for 8 hours or on high for 4 hours, until the chicken is very tender.
Remove the chicken to a cutting board and shred with two forks, then return the shredded chicken to the slow cooker and stir. Continue cooking on low for 30 minutes or on high for 15 minutes to allow flavors to meld.
Warm the tortillas if desired. Spoon about 2 tablespoons of the shredded chicken into each tortilla.
Top each taco with shredded romaine, diced tomato, shredded cheddar, diced avocado, and a dollop of plain Greek yogurt.
Serve immediately.