Mindfulness during sleep
Once the practitioner attains certain level of mastery in meditation and mindfulness, their sleep acquires a character of meditation. It's not like they don't sleep at all, but they do retain certain level of deep awareness during their sleep.

Specifically, when they see a dream, they know it's a dream. They remain aware of their body lying down on the bed. They remain aware of the content of their consciousness no matter how disjointed it gets during a deep sleep. If something happens around them, they wake up easily to provide their help if needed.

From my personal experience I can say this has gotten increasingly true for me over the years of practice.

As far as specific methods, stopping internal dialogue and mental gossip really helps mindfulness.