The Germanwings Flight 9525 tragedy [1] was effectuated by the suicidal pilot inputting an auto-pilot target altitude of 100ft, while flying over high mountains. The plane dutifully flew into the mountains, murdering 150 people.
While there are airports with elevations lower than 0ft, this is a good design question to ask. In general, it's assumed the pilots will do the right thing to save the day, if needed.