The UC38** SMPS controllers are almost always powered by an auxiliary winding on a SMPS transformer, not by the high voltage line it is switching. There may be resistors connecting the chip VCC to the HV line, but its likely to be a high value.
If the resistor is burnt so you can't see its value, then at least take a photo graph of it, as its size/shape will indicate whether its a power resistor, or simply a small signal bleed resistor.
As Frank said....560V? are you sure? Sounds like rectified three-phase power....