Everyone, remember it isn't cheating to do any modifications you want as DM.
Why bother having a thread if you're going to fiat declare that the problematic element isn't actually a problem? If it's not "cheating" to rewrite the world however you like, whenever you like, with no limitations, and concealing this from your players
while knowing that it would upset them if they knew you were doing it, what even is there to discuss? You've fiat declared that everything is fine.
Whatever you are trying to accomplish, try to be fair to everyone and develop your own style and procedures.
Okay, I think we need to clear up some definitions here.
How is it possible to be "fair," while also rewriting the world at any point where you feel like doing so? If you rewrite in a way that makes the players' goals harder, you are being unfair because you are setting the bar higher
because they're succeeding. If you rewrite in a way that makes the players' goals easier, you are being unfair because you are denying them the ability to actually achieve their goals under their own merits.
Either way, you are purposefully making their success
your responsibility, not theirs. You are denying them agency and self-determination; whether they succeed or fail depends in whole or in part on whether you
decided they should succeed (you chose to reduce the challenge, or chose not to increase it further) or fail (you chose to increase the challenge, or chose to not reduce it further).
Some good reasons to modify during the game are to a) keep a PC from dying (this is far and away the best reason), b) to end encounter quickly, c) to make an encounter last longer, d) to improve upon your work, and e) to keep the players guessing. They are all important tools every DM should embrace.
If you don't want PCs to die,
don't kill them. State that ransom is far more common in this universe, or that there is a thriving slave market, or some other reason why sentient enemies would not automatically kill all prisoners. Or, treat 0 HP (or even "dead") as merely "knocked out" or "grievously wounded" (presumably some kind of lingering penalty) as long as at least one member of the group survives to pull the rest out. So (a) is solved, without needing to do something you
know would upset your players if they knew it was happening.
(b) and (c), as Pemerton noted, are both trivially solved. (b) is solved by applying morale rules, having enemy units flee or surrender, or even just making some units fight poorly (perhaps because they are too scared and/or poorly trained to fight well). (c) is solved by fielding additional units. Reinforcements, wandering monsters or beasts, etc.; no need to fudge, just add an extra 1-2 of one of the things you're already using, or (for a "single big bad" fight) add in some local flora, fauna, or previously-used enemies. Everything is above-board, and the goal is still accomplished.
What does (d) have to do with fudging? You improve on your work by *understanding what you did wrong,* and then *correcting that mistake in the future.* Fudging, then, is
actively opposed to actually improving your skills as a DM. It becomes an easy crutch; "Oh, I accidentally made this situation too easy...WELP I'll just make sure nobody rolls higher than 5...and the monsters get some 'lucky' crits..." or "sh*t, the party's getting massacred. Guess the Big Bad Evil Gal just broke her sword by TOTALLY RANDOM CHANCE..." Either way, you're substituting actual learning for kludged in-the-moment solutions.
While I agree that fudging "keep
your players guessing," consider exactly how it achieves that: the players have information, upon which they base their choices. That information *is actually correct*...until the DM starts rewriting the world. Suddenly, their choices are now based on information which SHOULD have been good, but is now faulty. Whether this helps or hinders doesn't matter--they are no longer capable of making informed choices. You are "keeping them guessing" by invalidating their choices. That is not a healthy relationship between player and DM. Instead, you could "keep them guessing" in a variety of other ways. Challenge their preconceived notions: give them goblins and minotaurs and full-blooded orcs that are Lawful Good, sentient undead that just want to be left alone and have no interest in affecting the living, supposedly "good" elves who think genocide is the only answer, etc. Give them incomplete or conflicting information; never tell them the whole story. Force them to choose the lesser of two evils, or force them to support one "good" and thus violently oppose another. All of these are from the top of my head with no planning; if I were preparing for an actual campaign, I'm sure I could come up with both more things and more specific things.
So...no. I reject the notion that "fudging" is a tool DMs should use, and I completely refuse to accept the idea that DMs should outrightly lie to their players when asked a direct question. Honesty is fundamentally important to all human interactions. Doesn't mean you have to tell others absolutely everything, but lying should be avoided in the majority of situations, particularly when your statements--whether true or false--are the only information another person has for deciding what to do.