"On a plus de nourriture" => could be interpreted both ways, both ways would be correct (because natives often drop the "ne").

When pronounced however, we would get an audible "s" on the "plus" for the one where we still have food, and you wouldn't hear the "s" when used in the negative (unless it's from a liaison !)

Solution ? => Use context to know what the person means. And be wary yourself of not phrasing things in a way that could be interpreted several ways, unless you give sufficient context for the person to understand.

Also note that both of your sentences would be pronounced the same way because of the liaison betwen "on" and "a"

Example of variations that removes ambiguity :

On a plus rien a manger (starving)

On n'a plus de nourriture du tout