On the Qantas Flight 32 incident, the Airbus A380's number two engine encountered an uncontained rotor failure and partially damaged the controls of number one engine as well.
According to Wikipedia, engines one and four entered a 'degraded mode' after the explosion, and number one could not be shut off after landing.
So it seems that in case an engine loses all communication signals from the aircraft's control systems in the cockpit, it could somehow remain operational. To me that definitely sounds a lot safer compared to shutting down and risking losing all thrust.
So do jet engines, by design, keep producing thrust in case they lose contact with the control systems?