You drop the prisoner and try to run. That works for a short while, but you don't know the Deadmines as well as your pursuers. Pretty soon, you find yourself cornered again. You look around for anything you can use to your advantage. You can see the prisoner trying to get up, as well as a loose chain dangling precariously near you.
Fight back. Go out with dignity. Maybe it'll give your captive the chance you're passing up for yourself. Trip the chain.