。
She passed away peacefully in her sleep.
Literal
She [topic-は] during-sleep peacefully passed-away.
永眠する (えいみんする) is a euphemism for death — literally 'eternal sleep.' It's respectful and often used in obituaries and formal announcements. 就寝中 (during sleep/bedtime) establishes when it happened, and 安らかに (peacefully) describes the manner. The entire sentence is composed of elevated, respectful vocabulary appropriate for discussing someone's death with dignity. Compare the casual 死ぬ (to die) with this reverent phrasing.