In Dungeon Crawl Classics, there are two ways to save a dying character.
First, a character who drops to 0 hit points starts bleeding out, and continues bleeding out for a number of rounds equal to their character level (so a 0th-level character bleeds out instantly, a 1st-level character bleeds out for 1 round, a 2nd-level character for 2 rounds, and so on.) If a character receives healing while they're bleeding out (either from a cleric's lay on hands ability or from the new fleeting luck mechanic) then they lose 1 Stamina and wake up with however many hit points they regained. Healing a character who's bleeding out requires another character to step outside combat to administer aid (unless fleeting luck allows characters to heal themselves, I'm not completely sure how this new mechanic works.)
Second, a character who drops to 0 hit points might get saved if their friends roll over the body. The idea of rolling over the body is that maybe the character got lucky - maybe they weren't really dead with 0 hit points, maybe they were actually just unconscious with 1 hit point. The character who seemed to be dead rolls a Luck check - if they roll less than or equal to their Luck score, they get lucky, and they're just unconscious (if they roll over their Luck score, then they're unlucky, and they're really dead.) If a character is rolled over, they lose 1 Strength, Agility, or Stamina (at random) and they get -4 to all Action Dice rolls for the next hour. Like healing, rolling over the body requires another character to administer aid. Unlike healing, there's no time limit built into the rules for rolling over the body. You can attempt to roll over the body of a character you failed to heal who just bled out before your eyes - maybe they'll get lucky and it just looks like they're dead. You can also attempt to roll over the body of a character who got left behind when everyone else ran away from the monster that seemed to kill them, or a character who got dragged away to one monster's lair while the other monsters prevented the other characters from following - as long as you eventually find the body, no matter how much time as past, you can attempt to roll them over and see if they're really alive. (As a judge, I would probably still rule that 0th-level characters who seem to die are really dead and can't be saved. And I wouldn't let the other characters find the body of a fallen comrade unless I was willing to let them try to roll over the body and save them.)
I've written a Death & Dismemberment Table for DCC. (As far as I can tell, the idea and name of a "death and dismemberment table" originally comes from Robert Fischer's "Classic D&D Injury Table" and was popularized to reach a wider audience in Trollsmyth's "Playing with Death and Dismemberment." Since then, the idea has diffused and proliferated into numerous versions and rule systems.) To roll on this Death & Dismemberment Table, a character still has to be saved from death by being healed while bleeding out or by having their body rolled over to discover they're really still alive. Healing still requires clerical magic or fleeting luck, and rolling over the body still requires a successful Luck check. However, this table replaces the automatic ability score loss that accompanies healing or rolling over. Instead of automatically losing 1 Stamina (or automatically losing 1 Strength, Agility, or Stamina) the character instead experiences random ability score loss. On average, the results of this table are equivalent to the automatic 1 point loss in the DCC core rules - but only on average, any individual roll might produce results that are worse, the same, or better than the result listed in the core rules. Also, the way I've suggested deciding what dice to roll means that low-level characters are likely to get worse results than the following the core rules, while high-level characters are likely to to experience better.
DEATH & DISMEMBERMENT TABLE
Roll on this table after a character has been saved by healing magic, fleeting luck, or rolling over the body. The dice-type for the roll is determined by the character administering the life-saving aid, and the roll is modified by the Luck score of the dying character.
Most characters are untrained in medical care, and so roll a d10. Characters with the following occupations are considered trained, and so roll a d20 - alchemist, barber, butcher, dwarven apothecarist, elven sage, halfling chicken butcher, healer, herbalist, shaman. (Judges using alternative occupation lists should determine which occupations are considered trained in medicine.) Clerics always roll d20 + CL. Unless granted a superior dice-type by their occupation, thieves roll the dice-type indicated by their "cast spell from scroll" ability. (At the judge's discretion, thieves could recieve the dice-type determined by their occupation and add their "handle poison" bonus to the roll, but this decision should be consistent across all thieves.) Wizards who have an arcane affinity for necromany use the dice-type indicated by their occupation, but they may improve it by +1d for each one spell their affinity grants them the ability to cast using a higher die. (For example, a necromancer who got result 14-15 on the arcane affinity spell rolls a d12, while a necromancer who got result 26-29 when casting arcane affinity rolls a d16. The maximum benefit of this training is to roll a d30, which would require both a trained occupation and an arcane affinity result of 16-19 or higher.)
0 or less Internal bleeding / cerebral hemorrhage. Your injury is much worse than it initially appeared. Outwardly you look unscathed, but your insides are shattered and pulped. Despite all efforts to save you, you bleed out and die.
1 Stroke. You blacked out, and when you came to everything was dark and quiet. You are blinded (by a cutting attack) or deafened (by a bludgeoning attack) until healed and you permanently lose 2 points of Personality (if cut) or 2 points of Intelligence (if bludgeoned).
2 Spinal injury. You heard a terrible snapping sound, and now you can't feel your body or move it except to make it twitch or spasm. You are paralyzed until healed, and you permanently lose 2 points of Stamina.
3 Shattered elbow. You landed hard, and your arm bent at an ugly, impossible angle. Your broken arm is useless until healed, and you permanently lose 2 points of Strength.
4 Mangled hand. You broke your fingers, snapped your wrist. You'll never make such precise, steady movements again. Your broken arm is useless until healed, and you permanently lose 2 points of Agility.
5 Concussion. You passed out, you threw up. Your head is spinning, your vision is blurred, you can hear people talking but you can't understand the words. You permanently lose 1 point of Personality (if cut) or 1 point of Intelligence (if bludgeoned), and until your organ damage is healed, you cannot engage in strenuous activity (combat, running, jumping, swimming, climbing) without making a DC 10 Will save or else getting dizzy passing out.
6 Heart attack. For a moment your heart stopped and you couldn't draw breath. You vomited and shit blood. Even now it feels like your chest is being crushed in a vise. You permanently lose 1 point of Stamina, and until your organ damage is healed, you cannot engage in strenuous activity (combat, running, jumping, swimming, climbing) without making a DC 10 Fortitude save or else hyperventilating and fainting.
7 Slipped disc. Your spine twisted and your hip fell out of its socket. Your leg is numb and you can't feel your toes. You feel pins and needles when you feel anything at all. Until your broken leg is healed, your movement rate is reduced by half, and you permanently lose 1 point of Strength.
8 Shattered knee / broken ankle. You went down hard and now your leg can barely support your weight. You'll never be as nimble or as light on your feet as you were before. Until your broken leg is healed, your movement rate is reduced by half, and you permanently lose 1 point of Agility.
9 Nasty headwound. You have an ugly scar on your face now. It makes you stupid; it makes you mean. You permanently lose 1 point of Personality (from a cutting attack) or 1 point of Intelligence (from a bludgeoning attack.)
10 Broken ribs. Your chest made horrible cracking sounds as you slammed into the ground. You'll never draw a full breath again. You permanently lose 1 point of Stamina.
11 Dislocated shoulder. Your arm was knocked from its socket. You can put it back, but it'll never bear weight like it used to. You permanently lose 1 point of Strength.
12 Sprained wrist. Your hand got bent back too far, at an angle it was never meant to turn. It will always feel stiff and shaky after this. You permanently lose 1 point of Agility.
13 Success! You are revived without permanent injury.
14 Success! You are revived without permanent injury.
15 Success! You are revived without permanent injury.
16 Success! You are revived without permanent injury.
17 Superior healing! You moved faster than you've ever moved before trying to dodge that last blow. You failed then, but you won't fail again. Permanently gain 1 point of Agility.
18 Superior healing! You never saw such perfection in the techniques of violence until you saw the blow that almost killed you. Now that you've seen it, you'll fight more perfectly too. Permanently gain 1 point of Strength.
19 Superior healing! All your life you've had a crick in your spine; your bones clicked when arched your back, flexed your hips, turned your wrist, stretched your jaw. Somehow that last blow knocked everything into place, suddenly everything just fits and nothing is out of place. Permanently gain 1 point of Stamina.
20 Superior healing! You used to be callow and naive. Nearly dying has changed all that. You have perspective now. Permanently gain 1 point of Intelligence or 1 point of Personality (your choice).
21 or more Divine intervention / patron bond. Your recovery is nothing short of supernatural. Some powerful being had a hand in keeping you alive. It might have been your cleric's deity, your wizard's patron, or another supernatural entity trying to recruit you. You recover all hit points and permanently gain 2 points of Luck. In addition, roll 2d4 + 10; you gain that result in Divine Aid or from the appropriate Invoke Patron spell. You can gain this Aid or Invocation at once, or later at a time of your choosing. The entity owns you now; it saved your life, and you owe it a favor in return.