How to Disappear on Facebook
If you want to set up your profile so that no one can see you, you have to make it a limited profile. A limited profile is set up so that only people you want to see you can search for you or talk to you. In effect, you will have disappeared from Facebook, especially if you do not place friends in your limited profile. This extends to your picture albums, which disappear along with your profile.
Log in to your Facebook account in your Internet browser and go into the "My Privacy" tab.
Find the "Limited Settings" link in the "My Privacy" tab and click on it. This tell you what you are currently sharing at this time and how people are able to find you on Facebook. Every checked box represents your exposure to a search.
Deselect all of the options; leaving even one open lets others search for you through that feature. Hit "Save" and enjoy the anonymity.
Log out and make a fake account with Facebook to test your disappearing act. Do a search for your other account and see if it comes up. If not, you are done. If you do show up, then you left something checked and need to log back in and uncheck it.