To expand a bit on Mark's comment... I would say: "It depends..."
For the specific piece you described - if the "glaze" is peeling off, then I would have to assume that particular piece is NOT food-safe - for the simple reason that I would not want to ingest the material that's peeling. (I would also question whether it is actually a fired glaze that's peeling off - or some sort of paint or other coating that was applied after the piece was fired.)
For ceramics in general, there are several factors that can affect whether a finished piece is "food safe": Clay body composition, glaze ingredients; how it was fired, and even the current condition of the piece, all can make it "safe" or "un-safe".
One would have to know at-least the first two factors I mentioned, to even guess whether a piece is safe. Even manufacturers who label their clay and glazes as "dinnerware safe" state that "Tableware producers must test all finished ware to establish dinnerware status, due to possible variations in firing temperature and contamination."