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Don't even have to bury it. Just lay it flat coming out from the base of the pen and secure with some lawn staples and let the grass grow up through it. As Firefly said be sure to reinforce the sides of the pen, welded wire won't cut it against a dog or most any predator we have around here. The same lathe well secured with wood strips and plenty of screws, if a wooden pen, will work well.
A metal pen one can wire cattle panels over the original wire and stop a dog or large predator. That along with a good quality fence charger, non-pulsing, should stop nearly everything.
A long talk with the neighbor might help too and there is always the option of using rubber shot as they do with bears and even humans. The pepper spray that they use on bears will shoot a stream of about 35 feet but you have to watch which way the wind is blowing.