As much as I'd like to see looters in LA and MS getting the lead aspirin, I can't bring myself to countenance the death penalty for property theft. However, were I there with the proper equipment, I would be shooting the looted without hesitation. Not the looted stores, mind you, the looted property. A low-life is towing a big-screen TV out of a flooded Best Bayou (couldn't resist that one - sorry) and BOOM! One dead TV.
Possibly if the scum that's floated up on the flood water understands that their loot will be blasted out of their arms, they might develop something akin to a conscience. As if.