I'm currently revising an old story of mine. As I was reading along, I came to a place that I felt was more telling than showing, so I decided to expand it into a scene. I'm a pantser by nature, but even though I should be used to improvising scenes, it's still difficult to write one when you're not sure where it's going. (Just like it's difficult to write a blog post when you don't know where it's going.) Here are a few thoughts about what to do with unexpected scenes:
Add Worldbuilding Details: New scenes can give you the opportunity to take the story to different settings or expand on what you've already shown.
Show Character: One of the reasons I wanted to add a scene to my old story was to show more of the relationship between my heroine and her mother. Before, my heroine contacted her sick mother over e-mail, but given some of the feedback I received on another story, I thought readers might think that wouldn't be enough. So I had my heroine visit her mother before going off on her quest. This contrasts with how she interacts with her father, since their relationship isn't as good at the start of the story. I think it will be interesting to see how my heroine's feelings towards her parents change over the course of the story.
Take the Plot in a New Direction: This is something I'm still thinking about for this particular scene. It does add some conflict between my main character and her mother (I also added more conflict to the following scene). I think it will add some emotional resonance to the end of the story if I revisit this setting.
So, what have you done with your unexpected scenes?