Hit points go no lower than 0. There are no negative hit points.

@JeremyECrawford so, if the damage takes them past 0, but doesn't kill them, are they at 0 hit points?

— Ambryn (@konafusion) May 31, 2016

Hit points go no lower than 0. There are no negative hit points. #DnD https://t.co/Fa6GySIwtD

— Jeremy Crawford (@JeremyECrawford) June 4, 2016