Reduction in maximum hit points (max HP) is essentially 5e's replacement for the energy drains, level drains and negative levels of earlier editions.1 As such, it is not meant to be easily or quickly overcome, so low-level magic does not work. In fact, the 5e demilich's legendary action is called "energy drain" while many undead in 5e (specters, wights, wraiths) have a "life drain" effect similar to the vampire's bite. However, max HP reduction is not exclusive to vampires or the undead in 5e. Players can temporarily cause the same effect with the 6th-level Harm spell and other monsters have similar attacks that do not involve necrotic damage. The other max HP reducing attacks and their respective cures are:
- blue slaad's claw – unclear (involves disease), but maybe only a wish spell (MM, p. 276)
- chasme's proboscis attack – long rest or spell like greater restoration (MM, p. 57)
- clay golem's slam attack – greater restoration spell or similar magic (MM, p. 168)
- demilich's energy drain – greater restoration spell or similar magic (MM, p. 48)
- mummy's and mummy lord's rotting fist attack – remove curse spell or other magic (MM, pp. 228-229)
- night hag's nightmare haunting – greater restoration spell or similar magic (MM, p. 178)
- otyugh's bite – daily saving throw (involves disease) (MM, p. 248)
- succubus'/incubus' draining kiss – long rest (MM, p. 285)
As listed above, the means of restoring max HP are specified in the description of the ability/effect that causes the reduction to max HP. This is almost always powerful magic (i.e., the 5th-level "greater restoration spell or similar magic") or a long rest, the latter particularly for undead (specter, vampire, wight, wraith). However, a DM can interpret "similar magic" or house rule other powerful magic that can immediately restore max HP. For example, the blue slaad's claw and otyugh's bite create diseases that cause max HP reduction, so the 6th-level spell Heal may work since it "ends ... any diseases." Similarly, Heal washes its target in positive energy, so a DM could rule that it restores max HP to characters affected by the "life drain" of undead.
- The energy drain mechanic in AD&D 2e was the loss of entire levels and everything that had come with each (e.g., HP, proficiencies, skills, spells, etc.) while 3e imposed a -1 penalty on all skill and ability checks, attack rolls, and saving throws, -1 prepared spell and spell slot and -5 max HP (-1 HD). There is an EN World forum thread that anecdotally discusses the psychological impact of level and max HP reduction on players.
Designer's Intent
Mike Mearls tweeted that it should be a minimum of 1 point, but I can't find the same from Jermey Crawford. Mike Mearls talked about what was intended, but it isn't an official ruling:
no, should be minimum 1
Jeremy did weigh in about hit dice though:
You regain no hit points if you spend a Hit Die and your Constitution modifier reduces the total to 0 or lower. #DnD
If Mike is right about this spell, then the player becomes stable. If Jeremy's tweet about Hit Dice also apply to spells like cure wounds there would be no reason to assume that healing for 0 would stabilize someone, as the spell text doesn't say anything of the sort; but I think as a DM I'd let it.
Updated Text of Hit Dice and RAW
When the question was asked Jeremy's tweets were considered official rulings. Since then the text of regaining health from hit dice was edited in later editions since the question was asked to include:
The character regains hit points equal to the total (minimum of 0).
The text of the spell was not updated. So the only clues we have about cure wounds is the word "regain" in the spell, which implies it cant' be negative, and the intent text above. Unless a word has a special game meaning, the common definition applied. Oxford Languages Dictionary offers the following definition:
re·gain /rəˈɡān/ (verb)
obtain possession or use of (something) again after losing it.
"she died without regaining consciousness"
You can't obtain possession or use of negative hit points. Any argument must also use that common meaning standard. So when the rules say things like:
Healing
When a creature receives healing of any kind, hit points regained are added to its current hit points
It is telling you what to do, add them to your total, after you regain them. This doesn't change the meaning, define or redefine the word regain.
Best Answer
The extra damage does not count against the heal spell, but you made a mistake on your contingency trigger.
The dnd-5e rules basically state that when you take extra damage over your total, you're reduced to zero hit points and need to start making death saving throws.
So the order of things would be:
*BTW: Your contingency should state "When I get reduced to 1 or fewer hit points."
As originally stated you'd have to hit exactly 1 HP for it to trigger, allowing you to blow right past 1 to 0 when you take more damage.