Teosintes, the ancestors of corn, are very much alive, if not thriving.
Actually, the Dodo is an eminently non-obvious example, given that their meat was tough and tasted terrible. If they were routinely hunted for food, it must have been only because nothing more palatable was available.
Sailors will eat anything, I believe.
Regarding the dodo, remember, it’s not being eaten that makes the dodo extinct, it’s being killed. If a bunch of sailors stop off and kill some dodos, then discover they are unpleasant to eat, and leaves, allowing another shipful of sailors to arrive later, kill some dodos, then discover they are more or less inedible, and so on, dodos keep dying even though no gourmet meals were enjoyed. If the sailors aren’t diligent about spreading the word, every ship will try the same thing.
Also, I believe the introduction of pigs (intentionally) and rats (an accident, but not a surprise) to the island went a long way toward killing off the dodos.