sleep with one eye open

Some animals sleep with one eye open, so as to remain alert to threats.

sleep with one eye open (third-person singular simple present sleeps with one eye open, present participle sleeping with one eye open, simple past and past participle slept with one eye open)

1. (figurative) To remain vigilant at all times, especially by remaining partially awake or sleeping only lightly so as to avoid being caught off guard.

• “sleep with one eye open”, in Lexico, Dictionary.com; Oxford University Press, 2019–2022.