Maybe you get busy or just bored of the game, but you want to comeback later. It fine to take a break, fallout shelter vaults are quite resilient, but lets take a look at what does happen while you’re gone.
The vault uses resources for a short while after you stop, so resources will be lower on return. Not to worry, all your rooms will be ready too, so that will get things going again when you come back to the game.
There will be no disasters while the game is offline. Pregnant dwellers will give birth on return if enough time has passed. Any children will grow up. A number of other timers such as attribute training will continue and will be ready on return if enough time has passed.
What happens for dwellers exploring
Wasteland explorers will continue and will die eventually if you let them run long enough. It’s recommended to return them if you plan to leave the game for a long time. Recalled explorers will arrive back home. If you have left explorers out in the wastelands, not to worry they can be revived with enough bottle caps.
What happens for dwellers sent to quests?
Dwellers sent on quests will wait once they reach their destination, as you need to begin the quest manually.
As you may have figured out, the only real dwellers at risk are the ones left exploring. Everything else will wait for your return.