Pigeon drop is the name of a confidence trick in which a mark or "pigeon" is convinced to give up a sum of money in order to secure the rights to a larger sum of money, or more valuable object. In reality the scammers make off with the money and the mark is left with nothing.
In the process, the stranger (actually a confidence trickster) puts his money with the mark's money (in an envelope, briefcase, or sack) which the mark is then entrusted with. The money is actually not put into the sack or envelope, but is switched for a bag full of newspaper, etc. The mark is enticed to make off with the con man's money through the greed element and various theatrics, but in actuality, the mark is fleeing from his own money, which the con man still has (or has handed off to an accomplice).