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.