Aside from stabilizing wood through chemical means- petrifier, glues, epoxy, etc. or mechanical means- butterflies, other wood or metal fasteners...
When I ponder wood stabilization my mind goes to, and stays at, moisture content (mc).
Stable wood, to me, means ensuring there is as little difference as possible in the percentage of moisture between the surface, core, and everywhere in between. The overall amount of water isn't as important as the consistency of the water throughout. All seasonal movement is directly related to the amount of moisture in a board AND the varying degrees of difference within.
When the surface mc and the core mc differs by more than just a little, this is called "case hardening"
If you have ever ripped a board and had it pinch the blade (scary,right?) or have the two pieces coming out like bananas in opposing curves (sometimes twisting so badly the piece becomes firewood)- you have experienced case hardening. Splitting the board relieves some of the unequal tensions between the cells of the unevenly dry board (the drier cells are tighter and pulling together and the wetter ones larger and pushing). Then a new type of tension is created within each of the new boards.
Drying kilns combat case hardening by injecting steam into the kiln at the end of the drying process to equalize the surface mc and the core mc as much as possible. Impossible as it is to make 100% even mc across any board, this gets it close to the consistency of a multi-year air dry.
This is why, even when using equalized wood, you must mill your parts oversize- then work them back to square and true to their final size.
I have heard that some people will take a board they are about to mill down to final size and drop/throw on the floor in an effort to "pre-relieve" the board of some internal tensions... maybe works?
As a cabinet maker I am less concerned with whether my material has a total mc of 8% or 13%, than how much the content varies within each rough board prior to milling into smaller final sizes. Also, how much the mc varies board to board within the unit of boards.