Of course, perhaps you live in Detroit, and have 2014-era information, in which case you would know more than me. I merely decided to search for this because I recalled reading years ago this guy who wrote a blog article about his favourite Detroit supermarkets. (And the article above is that same guy. I suppose Detroit bloggers aren't that thick on the ground.) It certainly seems implausible that a city of 700,000 couldn't support at least one centrally-located food shop.
(I live in a city in the UK, population 500,000, and it has numerous grocery stores. As well as the ones I usually visit, there's one a mile away from my house - a decent size one to boot - that I never even knew existed until last month. I just drove down one particular side street to look at a house that was for sale... and there it was. You don't need a huge catchment area to support a grocery store, it seems.)
None of this is to suggest that Detroit is or isn't some hellhole...