no, they cannot shoot just for looting. even if told they could, most would refuse because they'd recognize it's an illegal order. this happened in new orleans after katrina. even under martial law, police/national guard cannot shoot looters simply for looting. in dire circumstances there will always be a few idiots who think they can. there were maybe a dozen looters shot by cops after katrina because they mistakenly believed they were authorized to do so.
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