Generally not on a large or long-term scale, but certainly on small and short-term scale. Agricultural peoples usually live at relatively high population densities, beyond what can be supported by a hunter-gatherer lifestyle.
Famine typically results in people supplementing their inadequate usual supply of food with items they don't usually eat, or don't usually eat much of. Non-hunter-gather famine foods include crops grown as animal fodder or for non-food uses, and parts of food items not usually eaten. For example, during the "Hunger Winter" in the Netherlands (their late-WWII famine, which killed over 25,000 people), people ate:
potato peelings
sugar beet
tulip bulbs
Their diet also include foraged wild foods such as:
In some places, such wild greens are regularly eaten by people living in rural areas. Famine results in greater use of such foods. Mushrooms are sometimes considered famine food - eaten during famines, but otherwise avoided due to fear of poisoning. A notable Scandinavian famine food is "bark bread", bread made by mixing flour made from the inner bark (cambium) of trees (often birch, sometimes pine and other trees) with normal flour (often rye in Scandinavia). One Finnish description of hard times can be translated as "the bread was half bark".
Similarly, foraging peoples (i.e., hunter-gatherers) will make use of less desirable foods when their usual preferred foods are in short supply.
Whatever animals are available are often hunted, including small birds, cats, dogs, rats, lizards, snakes, insects, snails, sea anemones, and more.
For more on famine food during the Hunger Winter, see