For the non-dice fudgers here: Do you alter what the encounters will be on the fly before the party gets to them? (e.g. If the dungeon was well balanced for a party of five and one just died... wouldn't the smart party always just leave to try and find someone with the PC aura at the appropriate level to join them to finish? What if the party missed all the places where there were vital clues about the upcoming big encounter because they did something you weren't expecting... do you give them some other way to find the clues you weren't planning on?) If yes, would you argue against my thinking that's still fudging, just at a different stage of the process?
Good questions!
1) I tend to run more or less level appropriate but sandboxy, so chances are the PCs are in a dungeon more or less appropriate for their level, but that's within a power factor of 2 or 3, and I don't scale encounters to party size. A larger group will have an easier time and/or can take on tougher challenges, but fights take longer and they get less XP.
If a PC has died that usually means a player has no PC (unless I'm running Old School with henchmen accompanying the party) so for that reason alone the PCs should retreat and get a new member, the new player's new PC. If they don't, not only will the party likely be too weak to survive - they are delving deeper in a dungeon that already killed one of them, while weaker than before - but also that player will be left out. So bad gaming and bad metagaming, too.
2) If the party misses all the clues or otherwise misteps and that leads to failure/TPK, I have no problem with that. I was just thinking this evening about a 20 session campaign that ended in victory for the antagonists and TPK of the PCs & allies present at the final doomed battle. From what I can tell, it all went wrong for them when they decided to detour from a scouting mission to launch a home invasion of the BBEG's estate, killing his wife and sister then firing the place, alerting his army camped to the north, while also destroying their moral standing with the BBEG's wavering allies. Basically a disastrous decision tactically and morally - but it made for a great story that resembled a classical tragedy. Fudging to ensure a different outcome would have made a far less interesting game.
Conversely, in my current campaign, the PCs' defeat by a dragon means they have lost the chance to discover a prophecy on the copper writing-plates it had stolen. They may still get the prophecy some other way, it's not a big deal, just some interesting foreshadowing of future campaign events. If it turns out they don't get it, or indeed those events never happen, then fine.