It may sound, somewhat, weird/odd/whatever you want to call it, but I was long pondering about this and I would like to ask you, based on your gaming experience: Have you ever seen the last/final/ending boss, in any game of any genre, who will NOT fight the player's hero (once the latter reaches him)? The reason for that would be either the boss would grow being afraid of the hero (seeing the hero’s capability of slaughtering all his minions in all span of the game previously, in order to reach him), or (better yet) to make the boss repent, to make him see his errors and change his worldview (to not want to conquer/destroy the world anymore, or any other evil purpose the boss might had).

As I describe it, the game would most probably be an RPG (and maybe with lots of dialogue) and the aforementioned result would be based on skill checks, but it could also be the default reaction of the last boss in other types of games too, as the developers designed it, to show that even a strong last boss could grow to be afraid of the hero (as the latter increases his abilities), or even that the most evil (boss who wants to conquer everything), could see his mistakes and become a better being, respectively.

If you’ve ever met a game with this situation, please mention the game with as less spoilers as possible, because I would surely like to see it!

I remember that about Max Payne, you are right! That's not what I meant that I am looking for, though you surely aren't fighting her!
I haven't played any of the first two Fallout games.

Edit: On second thought, one could say that she grew afraid of Max, and tried to flee the battle!! So, technically, you are right!

Edit: nevermind, because of your edit :P

Planescape Torment has various options for dealing with the end boss.

IIRC in Mass Effect 1, convincing S. that he'd been changed, and to shoot himself (instead of gunning it out) was an option... Never tried it tho.

Not ruining much of a story as it's not the strongest point of this game...
In Far Cry 2, the player ends up allying with the Jackal

Not 100% sure (since I've not finished it yet) but based on the ridiculous amount of (wildly different) approaches and solutions to every conundrum and problem - especially through dialogue - I've come across thus far I'd be surprised if it weren't possible to intimidate the big bad of Baldur's Gate 3 into submission or make him fear the player character to the point that he just throws in the towel.

Here are some for you:

Arcanum: Of Steamworks and Magick Obscura
- it is possible to reason convince the final boss and convince him to capitulate "defeat himself" without fighting.

Pillars of Eternity 2: Deadfire
- The final scene in the game sees you encounter Eothas. Depending on the dialogue options chosen by the player, he may "fight" you, or you are granted another ending.

Mother 3
- "Lucas. Bye. Thank you."

Shadowrun: Hong Kong and Dragonfall
- I have forgotten how these one's play out... but it meets your premise. You can talk down the final boss or obliterate them.

One that comes to mind that fits the description pretty well would be Rockstar’s Bully. If I remember correctly, the final boss keeps running away from you and you have to chase him up a bunch of scaffolding and whatnot before finally confronting him and fighting when he has no where left to run.

Doesn’t fit what you’re looking for perfectly, as you do end up fighting each other, but boy does he keep trying to run away from you before doing so!

The Witcher 2. You can spare the main villain without a fight and he will appear in The Witcher 3 if you imported your save.

Fallout 1 is a famous example. Spoilers:
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If you gather enough information and your character is a good speaker, you can convince the Master that "The Unity" is doomed to fail due to the super-mutants being sterile and he kills himself, skipping the necessity to fight him.

Requires several thing to be able to do it.

Potentially also SiN:
The main antagonist escapes from the protagonist in a cutscene instead of fighting.

(Spoilers, of course, including major Ultima 6 spoilers)

Ultima 6:

Once you get the gargoyle's prophecy translated, it turns out that a sacrifice of the Avatar (the main character) is required, but the term translated as "sacrifice" has multiple meanings. At this point, you go down to the gargoyle world, learn their language, and seek a peaceful resolution. The "boss" puts an amulet of submission, which is a cursed item (can't remove it, though it doesn't seem to have any adverse effects), around you, at which point the gargoyles are no longer hostile. Then, your final task is to banish the Codex, at which point the game ends with a peaceful resolution. The ending music is a mix of both Lord British's theme and the gargoyle world theme, which I think is rather clever.

Wizardry 3:

The "final boas" is an unwinnable fight, but once you solve the game's puzzles, you don't have to fight it.

Wizardry 8:

Don't know if this counts, but you have the option of siding with the main villain (who's been the main villain since Wizardry 6!), at the end. If you do that, you of course don't have to fight him, but you do have to fight a couple of your former allies (which is a much easier fight, apparently).

Honorable mention (even though it doesn't quite fit): Dragon Quest 1

Once you reach the final boss, he offers you a bargain, where you can choose to jointly rule the kingdom with him. If you refuse, the final battle starts, but if you accept, you can sort of get a different ending:
* In the original version, the game would give you a password that, if entered, would result in you starting the game over with poor starting stats. Then the game locks up.
* In the original English release (called Dragon Warrior), the game just locks up with the text being deep red, and you have no choice but to reset and lose everything since your last save.
* In remakes, you wake up at the inn, and the innkeeper mentions that you slept a long time and may have had a bad dream. In this case, the game continues.

For the games you mentioned thus far (I don’t know how to make multiple answers in one post):

- I played (the original) Planescape Tormet many years ago, and I was SO BORED with the ultra-heavy-text, that in the last 2-3 hours of it, I was just pressing the answers on the fly, barely reading whole sentences. I should admit that I wasn’t very good at English back then, but I’m sure I wouldn’t stand the game, even if I played it now.
- I had played the first couple of hours in Far Cry 2, but I was so tired of the extreme enemy respawn (as I later read, other people were too, and contrary to FC 1), that I dropped it.
- I have played Arcanum long ago, but I don’t remember that. I am planning a replay anyway.
- I remember that in Witcher 2, you are right! (I killed him in both my playthroughs. He made THE Witcher fail in protecting a King? He dies, whatever his reasons).
- I haven’t got (or tried) any of the other games you all mention (Mass Effect, Baldur’s Gate 3, Mother 3, etc.). I also think some of them are too old to be played nowadays, what with the plethora of games available (in all our backlogs) and the scarcity of time.

Same. He killed the guy I was protecting, let me take the fall for it, turned the witcher profession into political assassins for hire and essentially doomed the whole country. F*** that guy.