I'm not the most qualified to comment on this but I'll offer what I can:
In the city proper, I don't know that the 'old folks' thing will work well. The old folks still in Detroit in decent neighborhoods will not be areas with the cheap houses you are looking for (yes, there are some really nice areas in the city). The others probably left for nice areas outside of the city.
You'll probably want to look where the current wave of young people are moving to. I really don't know what these areas are but I'm sure you can look some up.
Midtown, with Wayne State University and the Detroit Medical Center, is probably a good area. Don't know too much about it but Tech Town[1] is at WSU. They are offering incentives to get employees to move and live in Midtown. I don't know that you'll find any super cheap housing there.
You could also look somewhere like Ferndale. It's just on the other side of 8 mile and maybe a 10-15 minute drive from downtown. You won't find the super-cheap $300 houses but you can find a really good deal. It's a nice, young, liberal town just on the border. It's also next to Royal Oak, a little more expensive area where you'll find a lot of young professionals. So that covers centrally located, safe and cheap, not super-cheap, but also not in Detroit proper, which also means lower taxes (as far as I understand).
I guess it all depends on your motivation. Finding something super cheap, centrally located and safe will probably be difficult.
[1] http://techtownwsu.org/