What part of the allegation is correct? The "inequality" part. People are unequal but the key issue is inequality of character, of ethics, of morals. We have inequality of outcomes in large part because we have inequality of ability, inequality of ambition, and inequality of gratification deference, in short, inequality of individuals and of subcultures.
Looting happens when the social fabric breaks down; when the network of systems that restrain the losers in our society fails for whatever reason. In short, whenever lowlifes believe they can get away with looting. An earthquake will do as a cause of chaos, so will a hurricane or a power outage or a riot. All have spawned looting.