The agency said that because of financial and computing constraints, some emails “that do not qualify as official records” had been stored only on individuals’ computers and not on servers, and that “backup tapes” from 2011 “no longer exist because they have been recycled.”To tell the truth it is almost impossible to loose an email (unless you work for IRS). There are also laws that require IT managers to make sure that copies of email are available for many years if not forever.
However, we are dealing with the government that already made trillions of dollars go poof. Just ask our president. He probably still can't explain where the stimulus money went to. The same goes for his friends who start those shiny new companies borrow hundreds of millions from our government and then POOF (the money disappear), and they go bankrupt.
So the short answer is YES. Even if it's impossible and ... illegal.
