This is something I actually have thought about. A few years ago one of my friends died and his Facebook page was bombarded with messages of consolation or people asking what had happened. It seemed odd because it was not like he was going to answer them back!

Facebook has realized that this is happening and they have decided that you can pick someone to take over your page when you die. The person will be able to post info to your page, respond to new friend requests (how many friends are you making after you die?), or download a copy of everything you've shared.  They're also offering an option where your profile will just be deleted after you die.

Because Facebook is Facebook, setting up a legacy contact requires finding hidden menus and jumping through hoops. Click the down arrow on the upper right hand corner of your profile, click settings, then security, then legacy contact.