If there is a measureable difference between motor loading with a torn belt compared to the drag of a good belt, you could set up an underload detector (actually an undercurrent detector) on the motor leads. ABB and Symcom make these for motors on mag starters. If the motor is powered by an inverter, some inverters have underload detection faults or one of the output relays can be set up as a current level detector. On the drives I am most familiar with (ABB) you can set up delay time on underload as well so you don't tend to get nuisance tripping.
In my experience, you have to be very careful about setting up the level detection to avoid nuisance faulting from routine operating conditions.