Heat the oil in a skillet over medium-high heat and brown the beef until no pink remains, 7 minutes; drain excess fat.
Add the onion and cook for 4 minutes, then stir in the chili powder, cumin and salt for 30 seconds.
Transfer the mixture to a 6-quart slow cooker and stir in the salsa, black beans and tomato sauce.
Cover and cook on low until the sauce is thick and the onion is tender, 4 to 4 1/2 hours.
Boil the shells until 1 minute shy of tender, drain them and fold them into the cooker with the corn.
Add the cheese by handfuls, cover and cook on high until melted, 8 to 10 minutes.
Serve as soon as the sauce coats the shells.