All natural materials move with humidity and temperature. This action tends to loosen knife handles. Stabilizing reduces (but doesnt completely eliminate) the movement. The benefit of stabilizing is a handle that is less likely to loosen over time. With woods, burl woods move more vs. straight grained woods. Bone or stag can benefit from stabilizing but less than wood due to cellular structure. Some woods move more than others. Some woods are so naturally oily they can't be stabilized reliably.
I personally prefer stabilized material but others don't like it for what they believe is a plasticy look the process brings to wood. There are lots of different methods to stabilize material. Some are more effective than others.