The Green Sun can disappear one day. It’s already gone from the perspectives of Earth C’s timelines. Without the Green Sun, a guardian could lose the power to safeguard a timeline. What are you going to do about that? Shouldn’t you try to find other sources of power in order to keep the Locked Timeline secure? Maybe creating your own eternal Green Sun? Are you willing to play Sburb yourself if it would mean ascending to God Tier, destroying a universe or two to create another Green Sun, or finding and doing anything to keep your friends safe?
You explain to the asker that they don't have to worry about the Green Sun from the perspective of The Locked Timeline. It exists as long as You do.
You elaborate that the structure of The Locked Timeline isolates it from Canon. Completely. It shares this feature with Als Black Hole, but unlike it, is non-permeable instead of only semi-permeable. As the guardian of The Locked Timeline, You act as this instance of The Green Suns steward, and host. To destroy your Green Sun someone would need to kill You.
