Yes, TRIACs normally fail short circuit, which is why they musn't be used for anything safety critical. There should always be another layer of protection, i.e. safety relay + contactor for motors, or thermal fuse for heaters, if an injury, fire or damage to property, could result if it failled on.
The MOC3083 is an opto-coupler with a TRIAC output and won't be used to switch the motor directly. It will be used to switch a separate TRIAC in series with the motor. It's possible the TRIAC, optocoupler, or both have failled short circuit.