When a person dies, what becomes of their digital self?

I logged into my Facebook yesterday, and was surprised.  Beyond the huge news that Steve Jobs, founder of Apple and leader in the modern tech revolution, had died at the age of 56, I also found news that a Facebook friend, who went by the digital name Ginger Snaps (real-world name: Melissa Hayes), had also died (the SUV she was driving crashed into an abandoned home, killing her and her cousin in the passenger seat).

Ginger Snaps' death surprised me in a weird way.  I am quite comfortable with death and loss (living without religion makes death far easier to deal with).  The reason I was surprised was because I felt myself unsure of whether or not the person I knew was really gone yet.  Let me explain:

In our modern world, with our social networking accounts and projections of ourdigitalselves through the internet, the person we project is not necessarily the same person we are in our real lives.  Melissa dies yesterday.  Her physical self is no longer extant.  But, much as we are preserved after our deaths through the memories of others and the impacts we've made in the world, her Facebook account still exists and her digital self is still there; silent, but there.  There are now many people posting their condolences and such on her FB wall.  It makes it seem like her account is still somewhat active.  I'm sure over the next few days and beyond, that traffic to her account will slow down to a trickle and then stop.  And her digital self will slowly fade as well.  But the account will remain active unless someone comes along and deactivates it.  Without someone to put an end to our digital selves after our physical deaths, then I suppose that digital self will remain, like a shadow.

Makes me wonder about where we're going.  The future is always far more exciting and surprising than what we ever thought possible.  Most people who lived in America in the early 1900's C.E. could never have guessed that we would have digital computers and internet with social groups which would allow for us to create digital selves.  There are always dreamers.  The sci-fi writers, the speculators, the scientists...  But our thoughts about what will come are usually only small tips of the icebergs that wait in the distance.