After their disastrous civil war, the titans removed themselves from the world. Seeking retreat and isolation, they now dwell in the Mountains of Purity high above Hughijen. Here they still monitor the world, looking for the building blocks or technology or magic that could one day lead to some other race repeating what they did. As heavy handed masters or at least self-appointed executioners, the titans live above the world so they can police it.
The majority of the people are convinced they know the truth, either that all the titans are dead or fled from the world or that the titans are alive and well and living in the Mountains of Purity. Those who believe the dead or gone myth believe that after the horrifying aftermath of the Titan War, nearly all of the titans who were still left alive fled the world in shame. Those who remained did go to the Mountains of Purity, but there they died off due to their extremely low numbers. Those who believe them alive believe that large numbers of them survived the war and made homes for themselves in the mountains where they live in seclusion to this day. They see no reason to believe that just because titans have not been seen walking the world for hundreds of years should they be assumed to be dead.