According to the Wall Street Journal, Facebook will allow you to decide what happens to your Facebook Page when you die.
Facebook legacy contacts will be able to manage accounts in a way that can turn the deceased person’s Facebook page into a kind of digital gravestone. Legacy contacts can write a post to display at the top of their friend’s memorialized profile page, change the friend’s profile picture, and even respond to new friend requests on behalf of the deceased.
If they’re granted prior permission, legacy contacts can also download an archive of posts and photos from the deceased, but not the contents of his or her private messages.
All of this is optional. If you do nothing, when Facebook finds out you’ve passed, it will simply freeze your account and leave posts and pictures at the privacy settings you determined, a process it calls memorialization.
Full article is available here: http://www.wsj.com/articles/facebook-heir-time-to-choose-who-manages-your-account-when-you-die-1423738802
