Excerpt from this article:
Facebook has a new feature for memorializing the news feeds of people who die: A digital will. The company will let you choose who, if anyone, has access to parts of your account after you die. Conversely, you can also tell Facebook to delete your account in the event of your death.
You can choose whether that person is allowed to download a file of all your pictures and posts for safekeeping. To trigger the will, your friends or family will need to put in a memorial request to Facebook.