If a marriage is based off the exchange of something edible, it would seem that the marriage would work as the edible item, if שוה פרוטה, would facilitate the marriage. But the problem arises when the edible food either becomes stale, and might no longer be שוה פרוטה, or when it is eaten, and is then definitely not worth שוה פרוטה.
Does the marriage not work at all? Is the marriage annulled after the fact, once the price of the food drops? (There are cases in גמרא כתובות where marriage is annulled in retrospect. I’m not sure where though).