Shaykh Salih al-Fawzan says listening to the Qur’an before sleeping is good. However, if you fall asleep and are not actually listening, then there is no benefit in it. The reward comes only when you listen and reflect.
This questioner says: what is the ruling on listening to Qurʿān from “Qurʿān Radio Station” whilst sleeping alone in my room?
If you are listening to it [Qurʿān], that is a good thing. However, if you are not listening to it and you fall asleep, then there is no benefit [in doing so]. Yes.