It's a fantasy setting where luck can run out

>It's a fantasy setting where luck can run out

How would you elaborate on this idea?

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mythic Iceland

Luck is a precious resource to be horded. Some people are naturally lucky a disproportionate amount of the time, some people just have rare lucky days. A very easy supernatural test is known widely enough that its folklore among commoners, and this test reveals how much luck you have right now. Like, you dip a white flower in a special solution while holding the stem, and the number of petals that the color sticks to is how much good luck you have, and the petals that fall off are the bad luck you have.

No one wants to have bad luck, and to make up the difference they will steal luck from other people any way they can. The wealthy or powerful keep a rolling ball of maxed out luck, which combined with their already impressive resources makes them virtually unassailable. No plan can work to the detriment of someone who is fated to have everything go his way for the next few days.

People with abnormally bad luck are ostracized and reviled, because no one wants to be caught in the crossfire of whatever inevitable tragedy will befall them. This does, however, make them useful tools if you keep them at a distance. A supremely unlucky man, in the right place, can topple a dynasty.

Bad luck exists to create good luck, and thus balance is restored.

Hit Points

Each person is born with a set reserve of luck, which may be positive or negative. This reserve drains like radioactive decay--e.g., each time you flip a coin, 0.01% of your current luck reserve is depleted, and your luck reserve gets asymptotically closer to zero (neutral).

In relatively-wealthy places, a person's luck reserve usually is discerned at birth with a simple magical test. If a baby is born with good luck, his parents typically give him a bunch of money and tell him to pick lottery numbers as soon as he gets old enough to understand what a lottery is (until then, he doesn't count as being able to "roll" on lottery tickets) until his positive reserve is depleted. If a baby is born with bad luck, his parents try to leave him alone as much as possible, lest he accidentally gamble away all their money. In these places, (1) half of the people used to be lucky but have traded their good luck for wealth, and (2) the other half of the people are unlucky and go through life desperately trying to avoid any situation in which their bad luck might damage their lives.

Because, in the long term, almost everyone in these places dies with either neutral luck or negative luck, the excess negative luck overflows into Bad-Luck Demons...

(In poor places where people can't afford magic tests at birth, good and bad luck are mostly equal. Though there's still a slight excess of post-mortem bad luck due to unlucky deaths, there isn't enough to spawn Bad-Luck Demons.)

Each person is born with a set "exchange rate" of good luck/bad luck. The lucky people may have a rate of experiencing amazing luck 10 times and then only suffering mildly bad luck 1 time before starting to become lucky again. It is not this linear or simple though, instead being able to accrue "debt" of bad luck amassing together into bigger incidents and eventually deadly accidents should the debt become big enough.

People in this world depend and calculate upon their luck. Knowing their rates of luck, some try to push it further to become really lucky in one great situation e.g. "A person is to attend a tournament and makes sure to seek out potentially unlucky situations to have a plus on their 'luck account'. The next day, he aces the tournament with the opponents simply having worse luck than the person in question had." In this example, the individual sought to be unlucky to further the chances of being lucky later on.

This has also lead to the common practice of immediately doing something important after having suffered a stroke of bad luck due to the belief that they're now in the positive.

The primary risks in the world are that you can't accurately predict your luck. Your exchange rate might leave you with 10 small minor incidents/humiliations or just combine into one massive disasters with you going blind and losing a leg in a freak accident.

Around the world, there are people wandering around, manipulating the luck of others, claming to be the ones of fate, that no amount of luck can change it. These are the primary antogonists of the world known as the Faters. They believe that those who try to amass and manipulate their luck to the better are dabbling into things that are not meant to be controlled.

The people that do amass large quantities of luck and live the good life still live in constant paranoia though, afraid that their bad luck "debt" will come back to haunt them soon.

A bit longer than first intended.

I'mma let you finish, OP, but I have to say my favorite luck system I've seen in an RPG is in Monster of the Week.
Nasty things tend to happen to PCs during a game, and bad stuff tends to snowball on you. That's okay, though. Everyone has a few boxes on their sheet for luck, (some more than others) and you can burn one of those to "fix" a bad roll, escaping from the consequences by sheer luck.
They don't regenerate, though. Every time you burn one, it's gone for good, and so you have to ration them carefully, and try to only use one when it will save your life, or where using one might prevent needing two later.
But as you go on, you find your luck boxes getting marked off, one by one, from the first one that's labelled "Okay" until you hit the last one, which is labelled "Doomed."

When you're all out, you are now Doomed. The GM is encouraged to skip the "soft moves" and go straight for the "hard moves" -- in Apocalypse engine parlance, this is the difference between the setup for something bad coming at you, and the follow through when it actually hits you. Like you don't notice the minefield until you hear the click underfoot, nor do you hear the monster until its claws are tearing at you.
At the doomed stage, the game starts to feel like Final Destination, where everything is out to get you. Your only hope at this point, if you're not one of the one or two classes that can get an extra luck point from a level up, is to get out there and find a real honest-to-god good luck charm and hang on to it for dear life.

Rock falls, everyone dies

Just one, huh? I guess you do only need one after all.