A dead pixel can have a very low output, independent of the amount of incoming light. A hot pixel can reach saturation even when no photon reaches the pixel. Warm pixels respond to the incoming light, but output different values that have no connection to the incoming light.
Most sensors have some defective pixels by their nature, which are listed in a blemish specification given by the sensor manufacturer. Some sensor manufacturers supply a 'map' of these defective pixels to the camera manufacturer so that substitute values from neighbouring pixels can be used.
Defective pixels can also form after the sensor has left the factory. It has been shown that cosmic rays can cause pixels to become defective, especially when the sensor is transported by air.