According to
Jim Jarmusch, director of the
film by this
name: "Down by law, at the time in the
mid-80s, was kind of in use on the streets as meaning a very close connection with somebody. If somebody was down by law, they were close to you or you would protect them. I know that, earlier, in prison slang, if somebody was down by law, and they
got out before you, they would contact your family or look after people
outside if you needed them to. So it meant something very close or a code. I really liked the contradiction of that, being something that sounds like being oppressed by the law, which of course under that condition is where the slang
came from. So, I liked that contradiction of it. And I liked it also in terms of the film being contradictory in that they are oppressed by the law but they also become down by law with each other."