Lee Willard

A rough criminal gets into an argument over a girl in a dance hall. The argument turns into a fight, and the criminal is shot. As everyone else looks on, a young woman comes to his aid, and it turns out that he is not seriously wounded. He still remembers the woman who helped him when, later, he is committing a burglary and gets a surprise that will change his life. (imdb)

Billy is held captive by an outlaw. (archive.org)

Dennis O'Hara is a poverty-stricken Irishman who believes (in typical movie-cliche fashion) that if he comes to America he will immediately land a job as a policeman. So he manages to scrape together the funds to get him to Manhattan, and leaves his sweetheart Katie O'Grady behind while he makes his fortune. Naturally he discovers that joining the force isn't as easy as he expected, and when he does finally get in, he winds up in trouble because of the graft collections of his boss.