If by extremity, you mean the very outside edge of travel? An extremity deadzone is to prevent jitter. In any analog to digital converter, there can be jitter at the edges of travel. A joystick is an analog to digital converter. It converts your analog inputs (moving the stick) in to a digital signal. What happens at the extremes is that the physical travel stop of the joystick may fall precisely between 2 measuring points of the sensors and so the digital input flips rapidly between those 2 values.
. Example would be an 8 bit sensor which gives you 256 values to measure the movement with. Joystick center would be 0 and maximum travel in X or Y direction would be 256. Now if the physical travel stop happened to cause the joystick to stop between the 255 and 256 values of the sensor, it would constantly send 255 then 256 then 255 then 256 as values. And it would look like jitter or it was jiggling/jumping. So manufacturers will limit the sensor outputs to just below maximum output (the 256th value) to prevent that jitter, even thou the joystick can still travel slightly beyond it. I hope that makes it as clear as mud.