There is a multitude of different reasons why the crime rate is constantly rising in Chicago. You could attribute it to the education system, the politics, the sheer population, among so many other things. However, when it comes to the business, layoffs may be a problem but I'm not sure that you can blame it on them not paying enough taxes.
If they paid more taxes, would that truly go back and help the population anyway? That's a whole other topic. But in terms of putting the blame completely on the 'large corporations' would be an exaggeration. In fact, more and more businesses continue to leave Chicago because of the violence.
Chicago violent crime causing corporate exodus (newsnationnow.com)