How to Stay Dead When Leaving a Dungeon in FFXIV
First of all, i need to say you can't stay dead when leaving a dungeon. If you're asking how to die in a town, table cloth from Balmung recently made a video guide. Searching reddit or google will bring it up.
If you're trying to do what I think you're trying to do: you have to leave the dungeon with several stacks of a DoT on you. Aiatar at the end of Brayflox Normal or Locksmith towards the beginning of Aurum Vale are probably what you're looking for.
You can't stay dead when you leave a dungeon, but there is a way to get what you want. You need to have two gear sets ready: your high level class and a class with lvl 1/low level gear. Go to wherever you want to be dead at and queue for Brayflox normal undersized party on your high level class (or any dungeon that gives stacks of poison). Blow through everything up to the second boss and kill lizard until Aitar drops down. Let me get a full stack of poison on you then kill him. After he disappeares, leave the dungeon. As soon as your out, switch to your lvl 1 gear and let the poison do its work.