Since per Jeremy Crawford's twitter and Is there a floor for maximum HP? you can get into a situation where your max HP is zero due to leveling up… what happens next?
What happens when your max HP is 0 because you leveled up with a negative Constitution modifier? Are you dead, unconscious, or what, and where do the rules say this? (The other question assumes death, but that isn't established as fact anywhere yet.)
You're not gonna die when you level
With the following release of PHB errata it has been clarified that you will gain a minimum of 1HP when you level:
This new rule ensures that when levelling up, you will not lose HP or create a situation where you are unconscious and unable to gain a HP because your max is zero.