In terms of what I do that definitely leads to player-generated fiction, when starting new 5e campaigns at higher levels, I've experimeted with asking the players to collectively write their characters' first adventure together as a short story (or an outline of a short story, if they prefer). It gives me a few already-established places and NPCs (in addition to those generated by players in their backstories), gives the players more familiarity with the other PCs' capabilities, gives everyone something to make in-character references to, and provides a ready-made explanation for where some of their starting magic items come from. Then play begins with what amounts to the second adventure.
In terms of what may-or-may-not count as player-generated fiction, a lot of gameplay at my table consists of me creating new content to be able to respond to player questions. The example used upthread of "is there a ladder?" isn't likely to show up at my table unless there was some obvious reason to expect a ladder to be present. But I might well see: "On our way in did we see anything that looks like a gardening or maintenance shed?" Or, at higher level of generality: "Are any towns along the road heading to [destination] large enough that it would be reasonable to expect them to have a temple to [diety]?"
I'll answer such questions consistent with what has already been presented, but quite often that means creating new details on the fly, especially if the questions represent an unexpected widening in scope (e.g. "What would I know about what faction Z thinks about the conflict between factions X and Y?") or concern hypotheticals (e.g. "What do I know about faction Z that could be relevant to what they would think about a conflict between factions X and Y if we're successfully able to start one?"). Because I'm the one authoring the answers to the questions I wouldn't have ordinarily have considered that player-generated fiction, but some of the early posts in this thread suggested it might count, so I figured I'd mention it.
In terms of what may-or-may-not count as player-generated fiction, a lot of gameplay at my table consists of me creating new content to be able to respond to player questions. The example used upthread of "is there a ladder?" isn't likely to show up at my table unless there was some obvious reason to expect a ladder to be present. But I might well see: "On our way in did we see anything that looks like a gardening or maintenance shed?" Or, at higher level of generality: "Are any towns along the road heading to [destination] large enough that it would be reasonable to expect them to have a temple to [diety]?"
I'll answer such questions consistent with what has already been presented, but quite often that means creating new details on the fly, especially if the questions represent an unexpected widening in scope (e.g. "What would I know about what faction Z thinks about the conflict between factions X and Y?") or concern hypotheticals (e.g. "What do I know about faction Z that could be relevant to what they would think about a conflict between factions X and Y if we're successfully able to start one?"). Because I'm the one authoring the answers to the questions I wouldn't have ordinarily have considered that player-generated fiction, but some of the early posts in this thread suggested it might count, so I figured I'd mention it.