Current State of End-Game Contents - A Blog Post from A Japanese Player

[Gormogon]

On RO, there was a boss teleporting when he had lost enough HP too. The arena was a huge corridor labyrinth, and you had to find him again before he had regenerated all his HP. Wouldn't be possible on FFxiv with the hard reset and the tracker though

Well it can be implemented but not exactly the same way.

Per se Fate boss reaches low level and teleports somewhere else in the same zone as it's phase 2 begins. You'll see the fate start somewhere else with a debuff that says, teleported like a coward healing its wounds which is a regen buff that mocks the fate.