You can bite your lip in your sleep though the chance is slim. Unless you are dreaming about something that can make you nervous thus you bite your lip. You will most likely never have that happen.
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Lips are a good source of nutririon and if you are malnurished your body might need the extra food!
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When you are sleeping, it may become a problem because you don't know how much pressure you are putting on your lip. If when you wake up in the morning and you have cuts on your lip, then you should consult a doctor.