The airframer needs to certify the operating envelop - and that includes below Sea Level pressure altitude performance. In most cases it's just paperwork, but sometimes you do run into issues - for example a FADEC that only has power setting defined to -500 ft. (you'd be amazed at some of the unintended consequences you can get when you exceed the table limits).
At entry into service, the 747-8F was certified to -1000 ft. - which everyone figured was adequate. Then Europe was hit with a very cold weather system and the pressure altitude at some airports dropped down to about -1,200 ft. The 747-8Fs were effectively AOG! There was some serious scrambling at Boeing to certify updated performance limits to -2000 ft.