(Domain of this topic: Games with character leveling, a hit point-like stat, and a stat that affects HP growth.)

Some games shave some stat that affects HP gains at level up. The stat has various names (I've seen Vitality, Constitution, Endurance, and Stamina used as the name for the stat), but they have a common function; the stat, along with level and perhaps factors like character class, affects the amount of hit points you get. For lack of generality, let's call the stat Vitality.

In many of these games, the hit points you end up with are affected by your Vitality, but not when your Vitality increases. Increasing it late gives you the same HP as if you increased it early. This is termed "retroactive HP gains", and the way I see it, is really the way games *should* work. Examples of this include Might & Magic 3 and onward, Wizardry 8. Dugeons & Dragons (including computer games from Baldur's Gate 1 onward), and many others. (Wizardry 1-5 actually approximate this, but the details are a bit more complicated.)

On others, your HP gains are affected by the Vitality you have at the time of leveling up. Raise it early, and you end up with more HP, in the ling run, than if you had decided to wait until later. Examples of this behavior include Bard's Tale 1-3, Might & Magic 1 and 2, Elder Scrolls series up through Oblivion (Skyrim got rid of the stat entirely, making the discussion irrelevant for that game), and way too many other games. This is termed "non-retroactive HP gains".

What I am wondering is if there are any games that fully invert that. Specifically, are there any games where you will end up with more HP, in the long run, if you wait until the last moment to raise your Vitality?

Maybe I need some coffee but... Huh?
What kind of game experience would that entail? Like a Dark Souls no-hit run and right before the end you finally spend some points on vitality? Hoping to be rewarded with an exponential explosion of HP right when it doesn't matter anymore?

Or could that be a necessary strategy to beat a game's final boss? That would require a matching game design with a relatively easy main game and a final challenge that is several magnitudes above everything you've seen before.
On the other hand, if game design forces this kind of play style, it isn't a "strategy" anymore (i.e. not player's free choice). Deviating from that path would render the main game too easy and the finale unbeatable. Oh, I don't know about that.

Regarding topic title: Isn't any word placed after "reverse non-" the same as using the original word or phrase? Reverse = opposite, non = opposite, opposite + opposite = same?

Answer to question: Personally don't know of any RPG, CRPG or ARPG, hybrid or variation, which backloads constitution, HP, vitality in manner suggested.

Edit. Sorta, but not quite. Taking the Healthy perk in Wasteland 2 at level 45 will give 45 HP while taking it at 30 will give 30, 20 at 20 and so on.

If you want delayed gratification...

Closest I could think: D&D 3e and Pathfinder 1e negative levels (gained after e.g, vampire level drain or losing a level from being resurrected) give a flat -5 to max HP until removed. That's potentially more than the HP gained for low hit die classes (like wizards).

I don't see it as even remotely the same type of thing. What you're describing is a status ailment, while this topic is about the fundamental growth mechanics. I've seen games that do this sort of thing. For example:
* In Final Fantasy 6, your equipped esper determines what stat you gain at level up. You have no espers for a while, and even when you get them, it may still be a while before you get the good ones.
* Final Fantasy 9 does something similar, but with equipment. I hear Final Fantasy 8 has passives that boost a stat permanently if you level up while the passive is equipped.
* Lords of Xulima has herbs that permanently boost stats. Thing is, the amount you get is dependent on your level in a certain skill, and they don't respawn, so to get maximum boosts you need to avoid picking them up until you max out the skill.