The player sandbox
The player sandbox has become very popular lately. Even some games that have a linearly progressing story will provide open areas for the player to explore and generally progress the story at their own will. Allowing the player to do as they will is a form of content generation. It is also the other way to procedurally generate story.
Hello Games' No Man's Sky is a giant sandbox that is meant for the player to explore. There is no formal story, per say, but the player will go on many adventures simply exploring the game universe. This is one answer to procedurally generating story.
The sandbox is also a good way to generate content simply by constructing some tools and letting the player build their own world. Keep in mind that procedural generation does not always mean random generation. Allowing the player to build their own experience has the same effect, if not providing more immersion, then randomly generating the experience for them.
Terraria allowing players to build...
