Safie's father, a Turkish merchant, was on trial in Paris for unknown reasons. It was generally suspected that he was being persecuted for religious and political reasons, rather than any actual crime. He was, however, sentenced to death. Safie's father offered Felix De Lacey Safie's hand in marriage, in order to help him escape prison. Felix turns down this offer, as he is in love with Safie & does not consider such an arrangement an expression of that love. But he does help Safie's father escape, for which he himself is thrown in jail. At this point, Safie's father betrays the De Laceys by returning to Turkey with Safie and leaving the family in jail. They are eventually released, but their fortune is stripped from them, & they are exiled from France forever.
There are several reasons why Shelley may have included this story in the novel. First, the ultimate kindness and generosity of the De Lacey family stands in stark contrast to everything the creature has known up until this point. Because of this, when they reject him as well, it is a deeper blow than the others. He had built a perfect arrangement in his mind, & the fact that this family behaves like all other people hurts the creature deeply. Also, Safie presents another female character in the story, one who has chosen her own independence and rallied against the male-dominated society (represented in this case by her father).
However, in a way, this story reflects cultural superiority on Shelley's behalf. Safie is from a non-Christian society that is presented as essentially treating women like slaves. Safie's father also becomes a stereotypical "outsider", a dark-skinned Turk with no morals. Safie's mother, who herself was a Christian, stands as Safie's model & guiding force throughout her life. Yet, if we look at the character of Elizabeth, Christian women had very few choices and control in their own lives. So there are many interpretations of this particular narrative.