A dangerous neighborhood is a relative description. If you had at least some ability to repair and rebuild, you make a go of it in a dangerous neighbourhood. Perhaps if you have the opportunity to redevelop, and others have the same thought, you could make a go of it in a place like Detroit or Buffalo or Cleveland!
The housing market has ballooned to such high prices that at the astronomically low price of $1,000, you would have more than enough money in the budget to dedicate to renovation and possibly sell it later for a much higher price if you don't feel comfortable with the neighborhood. Those prices have to be taken advantage of.
I recently read up on this article at home and I have to say I was surprised! This man landed on a very great deal even though he had to relocate to a dangerous area.. The way I see it is that when buying a house at that price you will arguably have enough money to set yourself up with a nice security/alarm system around your house in order to prevent break in or anything related to the dangerous area you're living in.
I would not re-locate to a dangerous area to save money. I was born in a dangerous area and I did my best in my 20s to get out of there. I love my family, but I had to move to a middle-class area a few years after college. I didn't feel safe or comfortable, and I wouldn't feel safe today either.