I saw an article in Pomona exactly about that - was it three years ago?
Goats had girdled trees. The gentleman bridge grafted over the girdling
and it worked - he did it in multiple places around the tree, so it
would have several grafts to work with.
Bad goats! BTW, I hear goats won't eat Paw Paw trees (didn't say fruit)
after they taste them in the spring...