They can move between zones just like any other card and continue to exist for the duration of the game
Elspeth Conquers Death, The Mirari Conjecture, and War of the Last Alliance come to mind
While this does combine them into one card and gives flexibility, it's not at the level of [[Denry Klin, Editor in Chief]]
However, it becomes excellent when paired with Mufasa, Betrayed Leaders ability, The Sun Will Set, which means that when this card is banished players can reveal the top of their deck and play it for free if its a character
If Kozilek is countered or otherwise leaves the stack in response to that triggered ability, the triggered ability will resolve as normal
If youd rather wait for Lorwyn Eclipsed details to be revealed officially, consider this your spoiler warning