You can farm and fish the entire undeveloped areas of NYC, but it won't be enough to feed or support the humans that live there.
You can say that for any metro area. Density will have to reduce immediately if there is economic collapse, and historically, when disaster strikes, that doesn't tend to happen immediately.
Also humans (especially large groups of them) need more than food: shelter, clothes, medicine, entertainment, education, religion, justice, law, etc.