...but how in the world do you burn a 1 GΩ resistor? That looks sort of like it could be a 1 watt resistor too. So back-of-the-napkin this would have to be from over a 30kV supply. So that sounds a bit off.
Unless it isn't. One hell of a bread maker then. I want one.
Only thing I can think of, maybe it's a bleeder resistor for that cap, and it failed by some kind of internal short which reduced its resistance (and increased its heat dissipation hence the blackened board)? But fails-short is an unusual failure mode for a resistor and 1 GΩ is pretty high even for a bleeder, so maybe we're misreading something.