A car with knock sensor will detect lower-quality fuel and pull back timing. This will usually limit your power, but not damage your car. My car manual even explicitly states that it won't affect engine lifetime.

Full disclosure, I still use premium anyway because I want to keep the car for a long time and I don't fully believe this disclaimer.

Generally you'll get worse fuel economy due to the ECU and knock sensor detecting the lower grade fuel and pulling ignition timing out. It's unlikely you'd even save money at the pump