In State of Decay, the player (initially) takes the role of Marcus who is faced with a sudden problem: the zombie apocalypse is here! While there is a series of main quests which lead the player through the game world, the focus is on surviving in the sandbox world.
The basic idea: Marcus explores the world and its abandoned settlements - either by foot or car - in order to scavenge food and weapons. The managerial aspects start when Marcus meets other survivors and opens up a base: then he not only needs to get more food to keep everyone fed, but also meet other needs like enough places to sleep. The base is expanded with modules which also can be upgraded - but of course this requires materials. It is also possible to found new bases.
Without bases, chances of survival are slim: Marcus fatigues over time which hampers his ability to fight and if he dies, he is dead forever. In those cases, the player can switch to another member of the community to continue playing. Each character also has abilities which improve with usage, e.g. a character gets better with melee weapons after using them for a while. Combat is action based and is strongly based on fatigue - when a character uses a weapon, it fatigues and can't fight as well anymore. This means single zombies don't pose much of a threat, but facing many makes it hard to survive.