Working with shadows can be harder than you would imagine. Shadows never lie, which makes it harder to hide mistakes in them. However, theater presents an interesting opportunity to use shadows in the art of story telling.
Now, for me there are two types of shadows in theater: Regular shadows cast by objects and people, and areas where no light is cast anyway. The latter is one of my favorites to see because it can add a certain depth to a scene. Case in point:
The design for Stages Theatre Company's Beauty and the Beast (2017) made the famous ballroom scene more personal for the characters with the use of a star screen and a light blue flood on the front of the stage, leaving the rest of the set to be hidden.
This lighting allows for Belle and the Beast to stand out from the set, giving the illusion that they've moved outside. It makes the scene more personal because it feels like natural lighting. There's nothing to make the characters look better, all they can see is each other.
Shadows can help deepen scenes such as the ballroom scene by keeping the set pieces from distracting from the actors. Audiences can still tell that it's a nice set, but their eyes are drawn to the actors instead.