if the bark above the girdle is still alive, a bridge graft (or a number of them around the circumference) can work. i've done it before on public-space trees that get weed-whacker-girdled. twigs from the top of the tree, grafted in to bridge the gap. how wide is the ring?
Here's one way to bridge graft. I'd've like to see a followup video to see if it worked. Just do some searches for "bridge grafting". It's not horribly hard and it sure can't hurt. Good luck!
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If the tree or branch is pretty small and not very high, you can pile up soil around it, and it may send out its own new roots, kind of like what happens with an air layer.
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