What is the trance-like state in which a subject responds readily to suggestion?
Good morning, Jennifer.
I believe that the term you are looking for is "hypnagogic." This is the stage between wakefulness and sleep. The goal of hypnosis is to place the mind in this state for a prolonged period. During this time, the subject is somewhat aware of the outer world, but can also experience dreams.
If that's not what you're looking for, please let me know.