Self destructing data here will be here considered to be encrypted data for which key available for limited time.
To have sharable self destructing one need to have keys that are available to everybody for limited time.
World wide web is large set of data that is evolving over time.
Web search result of choosen keywords is a hash of W.W.W. existing for limited time.
Number of unique choises of 5 keywords from set of 10^4 is approximately 10^20.
I assume that search results are not stored.
Thus if one chooses 5 keywords, hashes search results (through Tor on Duck Duck Go which does not bubble) with choosen password and uses it to encrypt data then distributes {encrypted data, password, 5 keywords} then he has self destructing data.