Rethink that.
For a set voltage, the VT (volt-time) product increases as the frequency decreases. It is VT that causes saturation. Take the worst case, DC. DC applied to a transformer will saturate it. Thus, a 120V 60Hz device operated at 120V 50Hz will see 120% VT. As long as the core was overdesigned so that a 120% voltage at 60Hz (144V) would not cause damage, then the 120V 50Hz should not cause damage. But, if the core was close to saturation at 120V 60Hz, it will saturate at 120V 50Hz.
I agree that a 220V 50Hz transformer can be operated at 120V 60Hz without problems. But, unless taps are provided, the output voltage will be useless.