No. It is not possible to get stuck in hypnosis, contrary to what Hollywood might portray. Hypnosis is a normal, natural state.
Some people believe that hypnosis is related to the hypnagogic and hypnopompic states that immediately precede and follow sleep. The hypnogogic state is that state where you are falling asleep, but are still aware of your surroundings. Perhaps you have started to see images or even dream, but still retain some level of present moment awareness. The hypnopompic state is that state that happens as you wake up naturally in the morning (without an alarm). Your body is very relaxed and maybe your eyes are even closed. You are asleep, but you are also partially aware of your surroundings. Maybe you can even follow a conversation in the adjoining room.
Just as people don’t get stuck in sleep, people don’t get stuck in hypnosis.
People who go “deep” into a hypnotic state (Eg. the Esdaile state) might feel so good that they don’t want the trance to end because they feel a natural sense of euphoria that is characteristic of VERY deep trance. Eventually, that person will either fall asleep or emerge from trance once the euphoria passes, in most cases within a couple of minutes, faster if a skilled hypnotist helps the person emerge.
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