The term screensaver is often used to describe the image that appears on the screen while a device sleeps. E Ink screens don’t need “saving” so the word doesn’t really make sense in that application, but others call it a sleep screen or wallpaper.
Whatever you want to call it, E Ink devices are unique in the way that they can display an image or text on the screen without using any battery power. An E Ink device only uses power when it changes pages.
See E Ink eReaders: The Best Screensaver is No Screensaver | The eBook Reader Blog
People have different preferences when it comes to what they like to have display on the screen of an E Ink ebook reader when it's turned off and resting in