The poor will always live where the prices are cheapest. Now that the inner cities are being rebuilt and the slums there are being replaced with mansions for the rich, the poor have to go somewhere. I propose they will go to the older suburbs and that this process has already started in large areas of the country.
Many of the suburbs were not built very well and have not held up to the test of time very well. As the poor and minorities move out into the most affordable housing available in the older suburbs, they will drive out the remaining middle class residents and speed up the process.