if a beagle sees game or gets on a scent, they could quickly move through the "shock zone" and then beyond the range of the fence. Once that happens once, your dog has learned it can cross the boundary and be free.
I've heard of beagles scaling chain-link. When we lived in Ames, our beagle tunneled out the back yard. But her digging phase is over now.
We had to put our family Welsh Corgi down about six weeks ago and the kids are clamoring for another dog. The best dog I have EVER owned was a beagle. He was Ohio-bred hunting stock; when he was a puppy he'd dig out from under our chain link yard fence. We moved to Minnesota and he learned to climb over the chain link fence. I didn't like the fence anyway, so I removed it and put in an underground dog fence. In less than two months he'd picked out the weakest point in the signal (farthest from the transmitter) and he'd run thru. I saw him gathering himself one day for "the attempt" and ran to the back door. I yelled just as he went thru and the goofy dog turned around and came back thru again! We later learned that he'd been leaving and coming home (thru the shock fence) on almost a daily basis. A neighbor called and said my beagle tore up his garbage. I said, "can't be, he's in the back yard and we have a fence." I went out to check him and he had a Chef-Boyardee can stuck on his snout!
Beagles are great dogs from every standpoint, but they are major league escape artists! Wonderful dogs and I wish I could take one off your hands, but my wife's just not ready after what we went thru with the Corgi :sad9cd: Good luck finding them a great home!