Why do resistors in parallel with each diode in a diode string prevent high voltage damage?
Diodes have reverse leakage current which means that each diode will behave a bit like a resistor of high value. If the reverse leakage current in each diode is not identical it means that their effective resistances will not be identical either and so the reverse voltage drop across each diode will differ.

If, for example, you had 60 volt diodes on your 100 volt supply and the voltage drops turned out to be 70 volt and 30 volt then one of the diodes would be stressed and may fail. Adding the parallel resistors with values lower than the diode equivalent reverse biased resistance will prevent the overvoltage by balancing the voltage drop across each diode.