No, there is no evidence in the Quran that mandates covering hair, and therefore, sleeping with hair open is not inherently haram (forbidden) in Islam. The Quran does not specify rules about hair covering during sleep.
Different Interpretations and Perspectives
While the Quran itself doesn't address this directly, different interpretations and cultural practices exist within Islam.
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No specific prohibition: Multiple sources, including Reddit discussions (https://www.reddit.com/r/Hijabis/comments/sxirza/is_it_haram_or-bad-if-i-keep-my-hair-open-at-home/) and Quora answers (https://www.quora.com/Are-women-in-Islam-allowed-to-sleep-with-their-hair-out-or-would-it-attract-jins), state that there's no Quranic or Sunnah (prophetic tradition) basis for prohibiting sleeping with uncovered hair. The idea of adab (proper etiquette) is sometimes mentioned, but this isn't a religious prohibition. IslamQA (https://islamqa.org/hanafi/muftionline/128524/women-sleeping-with-their-hair-open/) mentions it's "not in keeping with adab," implying a matter of personal preference and cultural norms, not a religious obligation.
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Context matters: The issue of hair covering is often contextualized within the broader discussion of hijab (modesty). While some interpretations emphasize complete hair covering in public, this doesn't automatically extend to the privacy of one's home during sleep. Many sources clarify that the hijab requirement applies primarily to interactions with non-mahrams (non-family members). A claim that the Shaytaan (Satan) plays with a woman's hair if uncovered is also refuted (https://islamqa.info/en/answers/143815/is-it-true-that-the-shaytaan-plays-with-a-womans-hair-if-she-uncovers-it-in).
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Personal interpretation and practice: Ultimately, individual interpretations and practices regarding hair covering vary significantly amongst Muslim women.
Conclusion
The decision of whether or not to sleep with hair uncovered is a personal one, rooted in individual understanding of Islamic teachings and cultural norms. There is no explicit prohibition in the Quran.