The Jorrocks sites has a useful glossary of hunting terms and gives two definitions for the term elope.

ELOPE: A halloo, to get hounds away, and also notice for men to come away.

Elope, or Elope forward awawoy (sic): When some hounds are gone away, to call the rest.

These definitions actually seem to contradict each other.

Whatever the word elope, it seems, is an actual hunting expression. Though none of the beagling or harrier people I know are familiar with the term.