>

My father works for the air force. Someone in his office once got in trouble for forwarding an email using an unsecured emailed address that included a nyt article discussing classified material. Had to retake a classified material training course. Poor bastard.
At the highest levels of classification, there are special rooms you have to use and all sorts of special procedures. 
At lower levels, these might be briefings written specifically for the person who has them, that just happen to include information from a spy or something. So it's very easy for no one to notice classified docs are missing.
Especially for the President or Vice President, so much is classified that I suspect it's pretty easy for things to get lost in the fray. 
I don't blame either person for having classified docs in general, the issue is when they are high-level Top Secret and left unsecured, and especially if you refuse to return them. 
The solution has to be that someone from the archives comes to review every document removed from the White House during a transition of power and signs off before they can leave. That's a lot of work but only every 4-8 years. You have to stop it from happening, ramping up punishments isn't going to do anything. >

It can be a lot less than that. During the Clinton email saga, one of the documents that was labeled classified was a call sheet for the Secretary of State. The classified material was that she was going to call a newly elected African leader to congratulate them. 
Low level classifications are a joke and are treated as a joke. It’s one of the reasons for Director Comey’s famous “no reasonable prosecutor would ever try to prosecute this”.

But a 2012 email released by the State Department appears to challenge that claim because it carries a classified code known as a “portion marking” - and that marking was on the email when it was sent directly to Clinton’s account.
The “C” - which means it was marked classified at the confidential level - is in the left-hand-margin and relates to an April 2012 phone call with Malawi's first female president, Joyce Banda, who took power after the death of President Mutharika in 2012.
"(C)  Purpose of Call: to offer condolences on the passing of President Mukharika and congratulate President Banda on her recent swearing in."

So after that, I’m just not very excited over prosecuting for classified material. It could be someone’s lunch order. They’re not going to tell you. >

It can be even less of a big deal than that. Sometimes publicly known information can be classified. I’m talking about articles in magazines and newspapers.