We used to live in Buffalo, NY. We lived within the city limits in an economically depressed neighborhood. Our neighbors paid $3,000 for a beautiful 4 bedroom, 3 bath home. It was a turn of the century home - 2 story Victorian style with hardwood floors, leaded glass windows, and huge front porch. The city actually gave them the house for free, the $3K was to cover the back taxes that the previous owner had defaulted on when he abandoned the house. The neighbors have since abandoned the house themselves.
This is actually fairly common in places like Buffalo where the local economy has been depressed for a long time and most neighborhoods within the city limits are viewed as undesirable and unsafe. A friend of ours bought an entire block of homes (again, beautiful 2 story victorians) for $10K. He's starting an urban farming community. Again - the neighborhood is severely depressed.