I would bet that a lot of South Chicago is like a lot of Detroit.
The neighborhoods become less desirable because they're perceived as high crime, so not only are people moving out, the homes aren't getting the maintenance they need and they start to fall apart. And then the neighborhood becomes even less desirable. There might be people paying rent on time, but they still have to leave because the landlord does not have enough funds to keep the building up to code.

It's a self-fulfilling prophecy, like Marty said. When the sellers all believe property values are about to go down, they will sell desperately. When there are more sellers than buyers, the property values actually go down. When the property value has gone down, and all the neighboring property values have gone down, there's no incentive to do maintenance.

The increase in crime comes later, after the actual poverty sets in.

---