I was in a similar situation some years ago. If the owner has truly as you claim, "fallen off the face of the Earth," and you have already attempted to contact them via the WHOIS contact information provided by the registrar of the domain, there may a "nuclear option" available to you.
The Registrar Accreditation Agreement (RAA) between ICANN and accredited domain registrars contains provisions to ensure the accuracy of the WHOIS contact information and places the burden of verification on the registrar. In particular, the relevant section of the current RAA states the following:
4 - If Registrar has any information suggesting that the contact
information specified in Section 1(a) through 1(f) above is incorrect
(such as Registrar receiving a bounced email notification or
non-delivery notification message in connection with compliance with
ICANN's Whois Data Reminder Policy or otherwise) for any Registered
Name sponsored by Registrar (whether or not Registrar was previously
required to perform the validation and verification requirements set
forth in this Specification in respect of such Registered Name),
Registrar must verify or re-verify, as applicable, the email
address(es) as described in Section 1.f (for example by requiring an
affirmative response to a Whois Data Reminder Policy notice). If,
within fifteen (15) calendar days after receiving any such
information, Registrar does not receive an affirmative response from
the Registered Name Holder providing the required verification,
Registrar shall either verify the applicable contact information
manually or suspend the registration, until such time as Registrar has
verified the applicable contact information. If, within fifteen (15)
calendar days after receiving any such information, Registrar does not
receive an affirmative response from the customer paying for the
Registered Name, if applicable, providing the required verification,
Registrar shall verify the applicable contact information manually,
but is not required to suspend any registration.
5 - Upon the occurrence of a Registered Name Holder's willful provision of
inaccurate or unreliable WHOIS information, its willful failure
promptly to update information provided to Registrar, or its failure
to respond for over fifteen (15) calendar days to inquiries by
Registrar concerning the accuracy of contact details associated with
the Registered Name Holder's registration, Registrar shall either
terminate or suspend the Registered Name Holder's Registered Name or
place such registration on clientHold and clientTransferProhibited,
until such time as Registrar has validated the information provided by
the Registered Name Holder.
This does not require the registrar to let you take over the domain of an AWOL administrator. However, it does provide you with an avenue to pursue. If you're unable to contact the owner via the WHOIS contact information for the domain, you can contact the registrar and ask them to verify the WHOIS contact information. Under the RAA, they are required to investigate. You can also express to the registrar your specific concern and hope that they'll pass it along in the course of verifying the information.
Be aware that if the registrar can't contact the owner, and doesn't feel like going beyond the bare requirements of the Agreement to help you out, this could potentially do more harm than good. That's why I call it a "nuclear option" - if for whatever reason the owner can't be contacted, the registration may eventually be cancelled. Maybe the registrar is willing and able to work with you to take over the domain in that case, or maybe you'll have to fight for it. And that's just the domain - if you don't have access to backup the site itself, you may have to deal with the host as well to avoid losing data.
I can't speak to the likelihood of success, as I've only gone partway through this process. In my case, the registrar was able to verify new contact information, which I used to get in contact with the owner. The site's founder had graduated college, gotten married and had a kid, and his mother was the one paying to renew the domain. Long story short, she transferred the domain, but I never got the data. So, a mixed result.