Hand hug is very popular among politicians, and when they choose to wrap your hand with their left hand, create a warm cocoon that protects your hand. When performed on the right person, they are considered warm, friendly, trustworthy and honest, and sometimes this handshake creates a hand-stack of 4 hands.
However, this kind of handshake is only done right with people who share a close bond, just like a hug, this handshake is seen as an intimacy invasion when done by a person who has just met.
You will also see some people using their left hand to hold the other hand from the forearms, elbows, biceps and even shoulders while shaking hands.
In fact, we reach out to shake hands to keep people out of our personal space and protect our bodies. The higher the arm of a person is seen laid their left hand, the closer the bonds that two people have (or at least the person doing the double handshake asks them to do it, or want to describe it, as in many cases politicians).