Let us say there's a level 5 fighter that has a 10 as his constitution score and 50 hit points. The fighter character gets into a fight and takes 40 points of damage, for 10 hp remaining.
Then let's say the fighter somehow loses 4 points of Constitution (for the sake of the question, imagine a DM's homebrewed poison that deals 4 points of Con damage/drain).
Now that the fighter's constitution score has dropped from 10 (+0 mod) to 6 (−2 mod), he would retroactively lose hit points based on his modifier times the current level: 2 × 5. His maximum hit point total would drop by 10 hit points and he only had 10 hit points left.
Would this situation drop the fighter to zero hit points because of the negative modifier to his constitution, or is there a rule that a character would have a minimum 1 hit point no matter what the constitution decrease is, until the character hits zero constitution and dies?
Best Answer
First: there is no such thing as ability damage in 5e. It is simply not a game term. There are not many official effects that even cause your scores to go down (related).
That said, if somehow your Constitution score does drop, the rules say:
Thus what you fear would not happen. Only your hit point maximum changes with your Con modifier, but your current HP is not directly affected.
It is not explicitly stated as far as I am aware, but it is consistent with some official abilities out there that if your maximum HP drops to 0, you die. This could happen as a result of Con modifier change if you rolled for your HP increases and were unlucky and/or your hit die is d8 or below and you drop to 1 Con (-5 modifier).