In an episode of the Korean television show “The K2,” which takes place in a world of fugitives and bodyguards, a man is being treated with a defibrillator when he enters into a dream state. On the fringe of death, he recalls taking a past love to a Subway restaurant and to a park for a picnic, where he gently feeds her a sandwich and soft drink with the Subway logo facing the camera. The detail is not a narrative quirk. It is a result of South Korea’s broadcasting regulations and the aggressive use of product placement in the country’s shows by Subway, the American sandwich chain famous for its $5 foot-longs.