In my opinion, the digital assets and the means to access them are the property of the estate. A power of attorney is invalidated by the death of the person granting the power. Generally, the only person who can direct the disposition of the assets is the executor of the estate. Appointment of the executor depends on whether the deceased named one or more in a will or died without a will. If the deceased was intestate (no will), a family member can apply to the court to be appointed. Usually, people don't bother doing this unless there is significant property such as land. These days digital assets such as a book manuscript or musical compositions can be significant.
I do not know if there is any case law on the question of whether a computer is just a machine or whether the digital information in the computer is an asset separate from the machine. What if a person left a will saying "I give my computer to X, but not the information stored therein which I leave to Y?" The civil courts would be asked to decide what that means and how to accomplish the division. That can be a problem even if you took out the hard drive, some digital tracks would remain. In criminal investigations, a computer is seized solely for the information it contains and that may be the analysis courts use to determine ownership after death.
Everyone should leave a will, name a responsible person who you believe will actually perform the duty, and leave written instructions for the handling of any special assets such as access codes and passwords and favorite personal items. This type of written instruction is binding upon the executor and the estate.
In many situations I would expect digital assets to include at least some intellectual property protections. In the situation of the death of the owner of those rights, those would become estate assets subject to all the protections of the probate laws in the particular state involved.
For a family member to "break into" a deceased loved ones computer gives rise to many complexities that will be quite fact specific. Who owned the PC, the decedent or the family member? Did the decedent leave a will to give instructions about testamentary intent with regard to the digital assests that were subject to the "break in". Answers to these and other such questions will dictate the situation.
I know of no caselaw in my jurisdiction that deals with a POA and digital assets such as a Facebook account.
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Adding to the discussion, we have added a clause within our testamentary documents, including Powers of Attorney, that allow the appointed executor/agent to access and terminate a web profile on various social networks including Facebook, and any licenses issued therein. However, even in death, Facebook may continue and the information (defined as User Content by Facebook) will be archived.
The Company may terminate your membership, delete your profile and any content or information that you have posted on the Site or through any Platform Application and/or prohibit you from using or accessing the Service or the Site or any Platform Application (or any portion, aspect or feature of the Service or the Site or any Platform Application) for any reason, or no reason, at any time in its sole discretion, with or without notice, including if it believes that you are under 13, or under 18 and not in high school or college. When we are notified that a user has died, we will generally, but are not obligated to, keep the user's account active under a special memorialized status for a period of time determined by us to allow other users to post and view comments.
As you can see, Facebook has the discretion to keep the account active (but it is not obligated to do so), when a person (user) dies. But equally important, Facebook has been granted a license (even if you are the owner), to keep the information entered by you as a user (i.e., "User Content"). By posting, uploading or emailing “User Content” the person has automatically granted to Facebook an irrevocable, perpetual, non-exclusive, transferable, fully paid, worldwide license (with the right to sublicense) the information to use, copy, publicly perform, publicly display, reformat, translate, excerpt (in whole or in part) and distribute such User Content for any purpose, commercial, advertising, or otherwise (very broad). And while you may remove your “User Content” from the Site at any time and the license will automatically expire, Facebook may retain archived copies of your User Content )(although the purpose is not clear why it would be retained).
I hope this helps...