Terry - the "rings" you count on a tree stump are the xylem (which carries water and dissolved minerals from the roots to the leaves). A new layer is formed every year. Outside of that, and just under the bark, is the phloem (which transports the sugars produced in the leaves by photosynthesis). When a tree is girdled as you describe, the xylem may still be functional, but the flow of sugars toward the roots thru the phloem is interrupted, resulting in a gradual root "starvation". This is why it may take several years for a tree to die after it is girdled. The bark is also a barrier to all kinds of bacteria and fungi, so the odds aren't very good that your tree will survive that kind of damage. Sorry!
