the sub can over heat if you send it too much power and will stop working if the coil opens,
you can check if the coil is open by using a multimeter. set to read ohms or continuity. if you don't have a multimeter you can use a 9 volt battery. just do a quick touch and release, if you see the sub go POP! and you see the sub move in one direction then the coil should be ok at least the voice coil is not open, they're could still have other kind of damage done to the sub. so if the coil is good, check your amp.