Well, that is a very general idea.
I mean, a lot of follow-up questions would have to be asked for context.
But first of all: Is this for a game you’re making or intend to make?
As for the idea: Sure, it has potential, but my mind immediately jumps to games like ‘Fallout: Shelter’ and ‘This War of Mine’.
But it all depends on the overall game as to what can and needs to be written for it.
If you want to pitch me a project with more details, you can also contact me directly.
It's alright. - It would just be useful to have the context.
What type of game? (Survival, resource-management, linear story, etc.)
Endless gameplay or a set story?
From what perspective? (First-person, third-person, single person, multiple people, specific characters, etc.)
Linear or branching story? - Mandatory or optional dialogue?
What kind of apocalypse? - War? Scientific? Mythological?
What is the situation of people?
How do they live? What do they have left?
What state-of-mind are the people in and what is their conflict?
From that basis, a story could form. - Good luck!
