Why have this rule?
It is a penalty for getting knocked out giving fights higher tension and realism (no more up/down up/down without consequence) and it buffs healing spells (now it isn't necessarily optimal to only heal once someone goes down).
Rule option 1:
When a character hits 0 hp you make a Constitution saving throw with a DC of 10 the first time. If you fail the save you gain a level of exhaustion and do not if you make the save.
Each subsequent time you hit 0 hp before your next short or long rest the DC increases by 5. i.e. DC 15 the second time, DC 20 on the third, etc.
This version mitigates the chances of gaining exhaustion somewhat and rewards characters with a higher Constitution with a higher chance of not gaining it since they're more resilient. Even with a Con save of only +0, a player would have a 55% chance of not getting a level of exhaustion the first time downed, a 30% on the second, and a 5% on the third knockdown.
Rule option 2:
We can use the less severe One DND exhaustion rules but you gain 1 level of exhaustion every down.
One D&D exhaustion rule:
Each level of exhaustion gives -1 to all attack rolls, spell saves, ability checks, and saving throws. You die if your exhaustion level exceeds 10. Finishing a Long Rest removes 1 level of exhaustion.
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