I'm running a 5e story.
Two players went into the crypt and got killed. My players manage their own sheets and the next day one player pointed out that he had not updated his saves after leveling up. He was 1 point short. He says he would have made the saves and wants to redo the battle.
What are the pros and cons of redoing it?
This is a case where you need to set ground rules which manage player expectations.
When you allow players to manage their own sheets, they are accepting responsibility for doing it correctly. Giving in to this demand sets the precedent that everybody else has to put up with fixing their mistakes. Mistakes happen in RPGs all the time — would they be happy re-running the scene if you had let them use some ability or power they shouldn't have been able to? Staying firm sets the expectation that they'll carefully manage their own responsibilities. You want to keep the game future-focused, not poring over past mistakes. If something is more than one turn in the past, it's probably best to move on.
Death is a part of the game. Risks need to have rewards AND consequences, or they are meaningless. Your players made the choice to risk it, they took responsibility for their sheets; it might be tough, but they signed up for it. If you give in to their request in this matter, it would seem that you're undermining their own agency.
That being said, I do recommend showing whatever reasonable consideration you can in response. It sucks to lose a character, especially due to a mistake. It doesn't hurt you to cut them some slack.
There are several implications to letting players redo an encounter, but I'll focus on a few important ones.
Players and characters alike generally don't know what is ahead of them. This is a very important tool for you as a DM, no matter what you're trying to accomplish. When players go back in, the encounter is not as good as it was the first time, since they know what is going to happen. The best part of any story or encounter is not knowing what might happen.
A hard part about role-playing is only using information your characters know. It becomes easy when the players know as much about a situation as a character does. But now, the players know about an encounter their characters do not. They will be tempted to use this information, and you need to make sure they're aware of this possibility. You may not care if they meta game, it is up to you.
A redo is a strong thing. We all wish we could go back in time and change the way we handled certain situations. A redo is giving your players that opportunity. Maybe this time they will be diplomatic (if possible) or they may find more information by talking to the enemy. Is this bad or good? That's up to you and what you're trying to accomplish.
Your players' characters have died. Or have they? This is a great opportunity for you to do some DM magic and tell a compelling and interesting story. There are so many things you can do besides letting them be dead. You can strip them of all their things and put them in a prison (yay, a new adventure!). You can resurrect them by some foul magic and give them temporary or permanent side effects. You can let them re-roll characters to later discover their old characters' corpses. The possibilities are endless! You lose this opportunity when you allow a redo. Be aware of that.
As user902383 has pointed out, a redo can also be an opportunity to tell a story. If you should redo, you can make it part of the campaign story, rather than an out of character decision. Make it a Groundhog Day type of situation. Whatever you decide to do, it would be in your best interest to spin a story out of it.
You mentioned he failed a save by 1 and that, had he updated his sheet, he would not have. There is no telling that he will survive this redo. He might just lose outright and the redo might be a complete waste of time. Not only that, but if they do fail the redo, they'll feel even more frustrated about it.
This is hard for any of us to say. It depends heavily on what kind of campaign you're running. If you're trying to kill your players, a redo is a big setback for you. If you're trying to tell a story, redoing an encounter might not be a big deal. Personally, it seems kinda sloppy, but such slop can be forgiven for new players and new DMs as you learn to play (if indeed you or they are new). I wouldn't let this type of thing happen more than once. I do think it's okay to redo a single turn if someone realizes they forgot something. Example, your player remembers their saves are different the next turn, so you give them a success and replay the turn from there. But after a session is over is just too far.
Out of game, as others have mentioned, they need to be up to date on their own character sheets. You can give them a mulligan if you want, but again, I wouldn't let it be a reoccurring thing. This can be a good learning experience without the sting of defeat. However, as you can see, the biggest implications seem to be cons rather than pros.
As the other answers state, letting them retry a dungeon from the start because of a minor number error on the character sheet sets a super-dangerous precedent, and it's likely the players will play more recklessly in the future since they can "retry". Errors happen. If it's half a combat round back, maybe you "change the past", but usually you just roll with it. In this case, I highly recommend rolling with it.
However, losing a character is a super negative thing. So, maybe we avoid that. My recommendation: Have a one-shot, one-off campaign where the players play alternate characters that run into the dungeon and pull out the dying bodies of the classic adventurers and help them recover. (Or, depending on level, maybe get the players resurrected) Then, normal play may resume, but the story is still advanced. Actions had blunted consequences, but at most only a minor history rewrite is needed.
Why would adventurers rescue the dying wizard? Any number of reasons.
There are two questions that are tied up together here and I think it is worth separating them.
In general, the assumption in a pen & paper role-playing game is that what happens happens.
In this respect pen & paper role playing games are closer to traditional board games (and sport) in that the game is played and the result is determined. This contrasts with the video game concept where the concept of trying over until you succeed is baked-in (lives etc. for platform games) or achievable through saving (role-playing games).
Deciding to move away from that paradigm is something your group is perfectly entitled to do. Just because this is not what most people do doesn't make it wrong!
If you decide that "yes, do-overs are a thing"; then that leads to the second question:
Ideally, you should decide this before it becomes an issue.
The rules for when a do-over can be called should be clear and unambiguous. You need to consider if this is something one player can call for, a majority of players or a unanimity of players. Can the DM call for a do-over for the monsters? If you like, you could even come up with house rules for "lives" or "saving" if you want; just like a video game.
No matter what you decide this will change the dynamic of the game and almost certainly have unintended consequences.
I think it would be unwise to allow do-overs for errors because almost every single combat in D&D, someone will make a rules, tactical or mathematical mistake.
In general, these will even out and are possibly more likely to be in the player's favour simply because the DM is having all of his rules, tactics and maths scrutinised by 4-6 players while generally only the DM is scrutinising each player. Player's tend to be more protective of their characters than the DM is of his monsters and will be looking very hard at things that cause them to die.
If you allow do-overs for that then a) there is scope for one in almost every encounter and b) some people will game the game; deliberately making mistakes so they can call the do-over.
What you might do is make a special exception this time because of extenuating circumstances1, but explain that it's a one-time deal.
Like several of the comments, I would prefer only doing a partial revert. Maybe they're alive, but all their gear is gone. Maybe they lost a level. Maybe their souls are trapped in limbo, and some god or other has given them a chance to fight in an underworld gauntlet for a chance at resurrection -- after which they're one level down and stark naked, if they survive.
Then in the future, their character sheets are their responsibility. My last group played that even if you just misread the sheet by accident, once the outcome was decided it was over. As long as a player isn't "accidentally" adding +5 to every roll, it smooths gameplay and prevents ret-conning two hours of story because of something silly.
If they accidentally won a roll because of a mistake, just think of it as a sudden bit of luck. If they lost, well, it was a bit of bad luck.
1I don't know your group, but if you're fairly new, and/or haven't really discussed your playstyle much, it might be that they're used to more leeway. Also, in this particular case they may have gotten their hopes up, so staying dead might be more of a letdown than if you'd just said "no" up front.
I'm assuming when you say they got killed, it was a TPK.
Is it possible, rather than a TPK, and rather than allowing a redo, it turns out that the monsters left them for dead, giant spiders strung them up, and they wake up hanging upside down?
I think there are two issues here. One is redo, the other is TPK.
Redo is a dangerous thing. As you're experiencing, Monday the the lawyers come out. It is occasionally useful to ret-con something. In an ongoing campaign, it is quite different to replay encounters or whole sessions.
TPK can also be a problem. Unless there is a clear expectation up front that that can happen, it can often really catch players by surprise, and GMs too, and it can end up being really not much fun.
The player make a mistake and paid for it. If you told the player that one of the monsters had a bonus you forgot about and should have wiped the party out, do you think they'd be clamouring for a re-match with that bonus included?
The reality of any RPG is that you're trying to simulate quite a complex reality, in this case not even our own reality which everyone knows well. Because of this everyone will make small mistakes, probably every sesssion. If you run re-dos for all of them you'll never get anything done and the game will be boring as all get out (speaking from experience here).
The DM has a responsibility to keep the game moving and if s/he makes a mistake that causes a PC to die then it's a serious problem that should be addressed, but if they also have to worry about checking every time a player says they made or didn't make some roll, the bonuses for which are on their sheet, then everything will grind to a halt.
Even if you do want to fix things, redoing is rarely the answer. It's boring for you, and probably for most of the players including the one that wanted the fix. It's better to say "oh, Ted's only 99% dead; take him to Miracle Max and you should be fine" and leave it at that.
The character's god (ie, the player) was not with the PC that day and did not step in to save them. Very sad, but that's the whim of the gods for you. Now, roll up some stats and get going.
Just to toss in a little side note, I thought I'd mention a few times I've lost a party member, and how I handled it without losing them or allowing a redo:
Once, the players were going mano a mano against some undead, when a particularly nasty ghost made a critical hit, and down went the bard. Thinking fast, I realized that the players didn't know it wasn't a wraith, so I say: "As you are struck down by the wraith, you feel your spirit eparate from your body, raising again as a wraith yourself. Suddenly, the mysterious amulet you have not yet identified begins to warm, and you feel your full onsciousness returning. You are now a wraith yourself, but you retain your intelligence, although unfortunately the amulet, having expended its power, is now destroyed." The players then get to go on a quest to find the mysterious and powerful good-aligned necromancer to restore his body.
So another time, the players were fighting a young dragon, when a party member made a bad roll, the dragon made a good one, and oops no more PC. He didn't want him dead, I didn't want him dead, but just saying "ok, nope, you don't die" would ruin the players agency by removing the risks of combat. So instead, I ramped up the difficulty - immediately bumped their enemy by a couple of levels (just low enough to make it seem they had always been that way), and brought in reinforcements for the monsters, turning it into a totally unwinnable battle, and forcing a TPK. Then they woke up, and it was all a dream...
In yet another battle, the players were question for an interplanar portal, when they had an unfortunate encounter with a certain subterranean race, and their glass cannon was shattered. "Luckily", it turned out that the portal was right around the corner, and oh look, there's a setting on it for the afterlife. What a coincidence.
The point of these little stories, is to highlight the fact that although you can't (or rather shouldn't) change the past, the future is still unwritten, and as long as you think fast, you can make out like you planned it this way from the beginning. You don't need to allow a redo to let a character be brought back from the dead - there are all sorts of ways that can actually happen, in-game. Others have posted some good ideas: He could be rescued by an NPC, or knocked out instead of killed, or anything else you can think of. These kinds of unexpected events make excellent plot hooks, and can spawn whole adventures of their own - who is this mysterious wizard, that swooped in at the last minute to save you? what does he want?
You pamper your players. Rules are rules and if the rules are bent around because someone just wants to replay then just have them replay with new characters. Tough to them.
