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The meter reads 4.4 ohms
The W is probably Wire Wound. Colors should be brown-black-black-silver for 1 ohm 5%. Then the 3 is 3W.
Probably an audio amp? WW is usually common and they normally break to infinity.
Might be a lead resistance problem.
If it;s wire wound, they usually open completely (e.g. Fuseable resistors). carbon tend to get larger in vlaue. Metal film puddles. Metal oxide usually breaks completely.
It's really a matter of feedback - the resistor is overloaded so gets too hot, this makes it's resistance increase, which makes it get hotter still - back to start and repeat
It depends on if the voltage across the resistor tends to stay constant or the current through it tends to remain constant. You would need to know where it was in the circuit and the nature of the initial fault that caused the resistor to overheat. My guess (As we have been given no information on it's function in the circuit.) is that is sensing current and something else has failed causing the current to increase above the normal level and something else (Other than this resistor) is now limiting the current. so I think P=I² R is more likely apply in this case.
Les.