This looks very similar to fusible resistors found as in-rush limiters in high power supplies.
Low power supplies can use a thermistor as an inrush limiter, but even at its lowered resistance can create high losses.
Therefore a high power supply usually employs a fixed resistor that is fully shorted out by a relay after a set time.
However...if for whatever reason the relay contact's do not close, the resistor will become cherry-hot and could actually cause a fire.
Thus, these types of resistors have a thermal cutout which will permanently open if the resistor's maximum temperature is exceeded.
Having said this, for a more accurate answer, would you kindly tell us the circuit you remove this resistor from?