If you drive down Woodward Avenue and into Detroit proper, you will see numerous grocery stores, but they're small independent operators. You won't see any large-scale name supermarkets. The small grocers charge more because they don't have the economy of scale that the chains have, but they're also willing to locate their businesses in a high-risk urban area. And they're armed.
But I digress. The Eastern Market in downtown Detroit is a wonderful source of fresh fruits and vegetables, among many other foodstuffs. And it's right there for anyone inclined to seek their wares.