Also, Some whites already lived in the ghetto then Blacks moved in to that area and it remain the same ( Fuller Park in Chicago, Brownsville for the NYers). While some communities remain middle class after demographic transition ( Chatham in Chicago, South Jamaica , Queens NYC , is that correct?). So therefore it's not always the case but nonetheless sometimes.

If you think you are too small to make a difference, you haven't spend the night with a mosquito.
- African Proverb