I am writing a book with the following scene in one chapter: It is trickling and my protagonists are outside looking into the night sky, looking to the stars. Reviewing the scene I am wondering: Is this possible? Can you see the stars when it is trickling, or even when it rains? Are there images showing this?
Yes you can. You just need a partly clear sky (to see the stars) and part cloud (to produce the rain).
For an example of suitable conditions, look for pictures of a moonbow. (I've only seen one once, personally.)
You can simulate this by going outside in clear weather, and spraying water with a hose. It is indeed possible to perceive stars despite precipitation.
However, where there is rain there are often clouds, which would be the bigger problem. But sometimes there is rain with patchy clouds.