The relaxed position of mammalian eyelids leaves them open. Muscles must contract for the eyes to be shut. Dead creatures cannot contract their muscles so their eyes remain open after they die.

You cannot shut their eyes for them by closing their eyes with your hand. Morticians place contacts in cadaver's eyes while preparing the body for a wake. Those contacts grip the inside of the eyelids so that they remain closed.

This is why some cultures have funerary traditions in which objects are placed over the eyes.

TL;DR: you and your loved ones won't close their eyes when they die.