In some cases, when a person dies, the jaw muscles and muscles surrounding his eyes relax, causing the mouth and eyes to open slightly, according to Willamette Valley Hospice. If the person dies in a hospital or other care facility, nurses or other attendants often shut the eyes.
In past times, people placed heavy coins on the eyes of the dead in an effort to keep their eyelids closed before rigor mortis occurred. According to a Business Insider article, the eyes of the dead tend to flatten shortly after death. Morticians often place eye caps over a corpse's eyes to give them the curved appearance people are used to seeing.