Hi there,
I'll resist any jokes like 'You must be kidding' oop's sorry.
Seriously though, If the goats had eaten right through the bark and cambium layer (which conducts all the sap etc) right down to bare wood, then I think the tree would eventually die but may live on 'borrowed time' for a year or two with the sap reserves already stored within the tree, above where the damage was caused.
I wonder if it's an option to saw it off cleanly just below the damaged area and with luck it may re-sprout from that point but of course to tree would have a more bushy shape to what you had before. Good Luck. Tbird+