“Except...they will be on their own in survival mode, in an area densely populated with terrified, possibly violent urban dwellers.”
I worked in Oakland, California during two disasters: The Loma Prieta Earthquake and The Oakland Hills Fire comparatively speaking, relatively few people were directly impacted by either. Nonetheless, in both instances, looters and predators of every stripe came out in force. Privation was not the impetus for their actions! No light, no heat, no food and no water would have really jazzed-up those activities!
Yes, anytime the criminal mind senses that the cops are too busy to pose an obstacle, crime happens.
In the event of even a mild breakdown of civilization, the cops will all be on traffic duty, minding every intersection with a light — and cleaning up after every accident that happens in the 99% of intersections they’re too understaffed to handle.