Crime is common when criminals can run free
Now let's say New Orleans is typical. The city has an evacuation order for a hurricane, of which 85% comply. The rest can't or won't which means 45,000 stay. What percentage of the 4,500 in the previously mentioned range would make up that 45,000 staying?
My guess is most of those 4,500 dregs of society would stay for reasons running from not being able to comply ('cause they've got no money or car or are still drugged out and sleeping on the floor of the sty they are currently living in) to wanting to stay (opportunity is knocking and they are salivating). That would mean the criminally inclined population of the city went from 1% to 10% literally overnight.
Add in the day-after belief that there will be no effective suppression of their criminal activities which is grows to experience-based knowledge in the next two days and what would you expect?
To top it off, percentage of the population that can't take care of themselves or can only barely do so, has risen, guessing, to maybe 70%?
It's the perfect recipe for what you see and shouldn't be unexpected. I certainly wouldn't lose faith in the whole population because of the activities of people I had no faith in to begin with. You do lock your home and car when you are away from them under normal circumstances, don't you? Why is that?
Even under normal circumstances, with the full population in their normal percentages, every city still has a sizable police force to keep the dregs at bay. What did you expect to happen when the normal population becomes so skewed, the police force is gone or fully occupied with an wearying array of rescue operations to task, coordinate and complete and the only rule that changed is "Nothing will be done to the criminals."?
You should expect crime to run rampant when the criminals are allowed to run free.