What happens to your facebook profile when you pass away? It carries on without you until Facebook is notified.
However, you can notify Facebook of the death on their website: http://www.facebook.com/help/contact.php?show_form=deceased
Once Facebook is notified, they will “memorialize” the account. Memorializing the account involves removing status updates, contact information and other information Facebook deems sensitive. Memorialized accounts are only accessible by confirmed friends and do not show up in search results to non-confirmed friends. The Wall of the deceased stays up to enable remembrances to be posted. Once an account is memorialized, login is no longer possible. So, you cannot login to your account from beyond nor can those who have your password and user name.
If you have a power of attorney and/or a will, I recommend you leave your executor and/or designated attorney-in-fact under your power of attorney with your passwords and usernames for your online accounts.