The Story Machine is a common storytelling strategy in many sandbox games like The Sims. It involves giving the player enough manipulatable toys and characters for them to create their own story from the gameplay (Schell 265). In this sense, it is very similar to the concept of emergence.
Jesse Schell describes this method in chapter 15 of The Art of Game Design: A Book of Lenses as one of the most common methods for conveying a game's story.