Facebook is allowing users to create what they call a legacy contact. This will give you the opportunity to grant someone permission to manage your FB Account after you have passed away.
From Fox news:
“In a statement released on Thursday, Facebook explained that it will memorialize the deceased’s account when informed that someone has passed away. The legacy contact will be able to write a post to display at the top of a memorialized Timeline. This could be used to share, for example, memorial service information, or a special message. The contact will also be able to respond to new friend requests from people who were not yet connected on Facebook, as well as updating the account’s profile picture and cover photo.” read more