“Keep multiple copies of the service running in different locations, but only accept modifications to the state in one location at any given time.”
This pattern is also sometimes referred to as failover or master-slave replication. You have already seen one particular form of failover: the ability to restart a component means that after a failure, a new instance is created and takes over functionality, like passing the baton from one runner to the next. For a stateful service, the new instance accesses the same persistent storage location as the previously failed one, recovering the state before the crash and continuing from there. This works only as long as the persistent storage is intact; if that fails, then restarting is not possible—the service will forget all of its previous state and start from scratch. Imagine your web shop forgetting about all registered users—that would be a catastrophe!