One thing you may not be taking into account: the urban underclass is economically unproductive. They DO NOT have the skills that would enable them to earn an income that would allow them to feed and house themselves in a free market economy. They can only survive (at what they consider a minimal economic level) by looting the middle class, either directly through crime, or indirectly through government benefits.
For the last few decades, the middle-class has been buying peace through the use of welfare. When they see that peace can no longer be bought, there is no further incentive to pay for something that is not being delivered.
So what happens when the middle class, while it is still a voting majority, decides to end the looting?
At the very least, enraged and starving urban dwellers can hold the critical infrastructure running through their areas hostage. They will snipe at highway traffic and landing airplanes, they will sabotage rail lines and pipelines and fiber-optic commo cables, etc. They can cause massive disruptions to the outside society simply by sabotage, in order to demand the resumption of free food.