The Heath Hen lost the war and is now extinct thanks to hunting, fire, disease, feral cats, fox, and development.
In the end, they killed cats in droves to protect the birds, as this gibbet suggests, but still they kept coming until the Heath Hen was no more.
But is that all of the story? I argue it is not. The Heath Hen, after all, was not a species, but a subspecies of the Greater Prairie Chicken, which still exists. If anyone wants to "reintroduce" the Heath Hen back to Massachusetts, or any of the states with scrubby heath barrens along the North American coast from New Hampshire to northern Virginia, all they have to do is have the right habitat and cover free of feral cats, fox, dogs, hawks, coyotes, bobcats, and other predators. Good luck!