Is a charred resistor open or short?
When resistors overheat, a variety of things can happen, some of which will increase resistance and some of which will decrease resistance--typically by creating alternate current paths.  Overheated resistors are not particularly likely to ever represent a "dead short", but high-value resistors may have their resistance drop by multiple orders of magnitude.  Note that subjecting a resistor to sustained moderate overloading may yield very different behavior from subjecting it to severe overvoltage conditions.  If an overvoltage condition causes an arc within a resistor's insulating material, the resistance may be greatly reduced as long as the arc is sustained, and the susceptibility to arcing may be permanently reduced, even if the resistance under low-voltage conditions is relatively unaffected.