The burden resistor may have been in the reactive compensation circuit or droop circuit. As the resistor starts failing and heating up, the feedback voltage to the regulator drops. The regulator senses a lower voltage so it boosts the excitation. That increases the generator voltage and var output so the resistor sees more current, heats up more and lowers the AVR sensing voltage. It can be a runaway condition. Hard to tell if the resistor went first or failed in response to another failure that boosted the generator output.
We had a VT fuse failure that sent the AVR to full output. The stiff utility system kept the voltage and var output in check, but the current went high but still below the relaying pickup. The feedback resistor finally failed. Since it created the most smoke, we initially thought it failed first.