My guess is that the movie is Sin which deals with Italian immigrants to the United States...according to the American Film Institute summary:
When Rosa, an Italian peasant girl, meets the attractive, wealthy Pietro, the head of the Camorra, a New York crime syndicate, she deserts Luigi, her fiancé, and departs for America. Hurt but determined, the simple, pious Luigi follows his sweetheart to New York. To prove his love, Pietro tells Rosa that he will steal the jewels of the Madonna for her. Impressed by this seeming devotion, Rosa informs Luigi of Pietro's boast and he, not to be outdone, decides to steal the jewels himself. After Luigi presents her with the coveted gems, Rosa makes her way through the Festival of the Madonna to find Pietro at Camorra headquarters. When she arrives, the theft has been discovered, and a mob is forming to hunt the culprit. Rosa begs protection from Pietro, who throws her out into the street. Overcome by religious guilt, Rosa collapses in a deranged stupor, then after returning the jewels, Luigi kills himself on the church steps.
My only basis for this comes from the clothing of the man, however the pictures I have from Sin show Theda Bara in different make-up and costume styles than I see here. Also the male actor does not match the appearance of the Sin pictures I have. Still, it still seems like it is possible. It might also be from The Devil's Daughter which came out June 16, 1915.
This image came the May 1916 issue of Photoplay magazine but, unfortunately, does not say anything about the picture other than Theda Bara's name!