All mortal minds shook, ever slightly, at the Endless Dream's passing. But Dream was just that, Endless. It would be a paradox if that which is Endless, truly ended. Therefore the old consciousness of Dream faded into backlogs, so a new Dream could be born.
It was Death that the new Dream met first because, like with any good story, the New Dream's life started with his death.
Alternatively: Morpheus croaks and a 17-year-old becomes the new personification of dreams. At least he'll get a new loving and supporting family... kind of.
Marcus struggles to make ends meet in a crumbling household and a dangerous town, but regardless, he loves his life. It is his version of normal and he will stop at nothing to defend it.
When the world he knew is ground into a fine sand, he uses the power of the soul to survive. He is now a heretic of this new world and struggles to create a new "normal" while accepting that he took his past for granted. He pushes forward in this accursed world. Will he let go of his old life or join with it forever in death's cold embrace?