It's not necessarily one play or any certain kind of play. You increase your odds of getting hurt the more you get hit. Getting hit while throwing may be more dangerous, but when you throw, there isn't a guarantee of getting hit. When you run down field there almost always is.
Your last sentence isn't necessarily true. The more guys you keep in, the fewer guys they have to cover downfield, and the more guys they can use to rush the passer. Or the fewer guys they have to cover, so the harder it is to get someone open, so the longer the QB holds the ball, and then you have a better chance of a defender slipping into the backfield.