Although there's not a lot of people willing to talk about it, the only real problem in Jackson is the same problem that hit New Orleans, Memphis, Birmingham, Atlanta and a number of other Southern cities and that's the white flight movement that began in the civil rights era.
Before the civil rights era, there were any number of immoral and now illegal mechanisms in place to keep black people out of the middle class and when they started to gain political but not economic power in the seventies, the almost all-white middle class decided they were no longer welcome in cities with a bi-racial power base, so they packed their bags and bought up little towns outside the city limits. Since they were the only people in town, the move gave them both the political and economic power they desired.
The move left cities like Jackson and Atlanta and New Orleans with a population overwhelmingly skewed to the poor and black who couldn't afford to relocate. Pretty soon, what black middle class there was began to move out of town as well making the problem even worse.
Cities work best when the middle and working classes are the largest and the poor and upper classes are the smallest. The white flight phenomenon, combined with the unnatural class distribution leaving most blacks either working class or poor, left cities with populations skewed to the poor and working classes.
The problem with this population model is that the poor and working classes require the most public services like police and public schools, but have the smallest tax base to fund it, leaving a real gap between the sources and needs of public funds. This gap between sources and needs materializes in the city with a spike in crime and school related issues like drop-out rates and low test scores.
At the moment, there's few constitutional ways of combating the problems of gentrification and white flight. I think you can legally and morally face the issue though, but first you have to be really honest about what the problem really is.
In the South, that means being willing to share power between white and black. Sharing isn't any easier when you're an adult than it was when you were in kindergarten, but it's still absolutely essential. More white faces among city officials in Jackson would go a long way toward slowing and reversing the white-flight trend. At the same time though, white residents have to be willing to accept black people in positions of power and not pack their bags for Madison when they see how black the city council is in Jackson.
This concept of a peaceful co-existence between races and cultures might be some sort of liberal pipe-dream of mine, but surely people realize the alternative can't last forever. Sooner or later, this pattern of black central cities ringed by white mini-cities is going to collapse in on itself.