A faulty brine valve assembly or damaged rotor valve can cause a water softener's salt tank to overflow.
The brine valve assembly should shut off water flowing into the salt tank when brine water reaches the correct level. Replace the brine valve assembly if it doesn't shut off fill water causing brine water to overflow the tank.
A damaged rotor valve can leak water into the salt tank causing water to overflow the tank. Check the rotor valve for damage and replace the rotor valve if it leaks water into the salt tank.