Buddy from your posts sound like a wonderful dog.
If Buddy not being well cared for
by his owners, than I agree with
others about calling a non-kill rescue.
If Buddy is well cared for, than maybe you can
work something out with your neighbors to
hole proof the fence which is quiet easy but labor
consuming.

Two things Your neighbor can do for a wood fence.


Buy Chicken wire and staple gun it to the bottom of the fence,
approx. 1 foot up the bottom, you should have approx.
2 feet of chicken wire left free that you can either
dig a trench and lay bricks or anything heavy on top
on the chicken wire on the ground
than fill up with dirt. What I did
was simply lay the excess chicken wire down and
lay rail road ties accross the chicken wire instead
of buidling trench, but it kept rocy, from digging
to the other back yard.
Bad example: L <--- the fence with chicken wire attached.

Another thing I did was to dig a small trench and fill
it up with cement right by the bottom of the fence.
I left enough room so the cement was not touching
the fence for repair and drainage reasons.
The dog can not dig through chicken wire or cement.
Just have to dig the trench far enough down to
discourage digging.
This worked for us and was not costly accept for
the rail road ties. Good luck with your neighbors.