Nuzlocke rules vary from player to player and there are a lot of fancy variants nowadays, so not sure how a rom hack could have things like that built-in. Afaik rom hacks have no way of limiting your captures to only the first encounter in each route. And coding the fainted = dead mechanic would be bad for several reasons (players who don't count death during training or during specific events, revive clauses, etc.) better just box/release your fainted Pokémon.
There are rom hacks that take nuzlocke and other challenges/playstyles into consideration by giving you mechanics to drastically reduce grinding, more capture areas, easier levelling, very friendly move/egg move relearning, Nature changes, Ability changes, etc. But no actual built-in Nuzlocke mode. Check Radical Red's Minimal Grinding mode, Unbound's Sandbox mode, or Inclement Emerald for instance.
