it was probably just a matter of time before she dug out. Beagles LOVE to dig, dig and dig some more. the chain for a couple of days thing sounds like a good idea. We had a beagle come up to the house about a year ago. Of course she was limping. It took 3 days to get a hand on her before i could get her to the vet. Long story short,,,, femur fx overlapping about 3 cm's, pelvic fx in 5 places, lots of stool from eating bones, and the usual electrolyte screw ups that follow dehydration. After an enema, bag of fluids and 3 weeks of laying on 4-5 inches of cedar chips she came out one morning looking for breakfast and running around the yard on her chain. Now she does great, but DIGS LIKE CRAZY.
hope everything turns out well, keep looking! and check the local pound, you can probably call them and leave a description.
cya
brad