The Janitor, knowing that the clone had no place in this time, sent Josie's clone through a portal. The clone appears as a hooded figure in multiple episodes and, in particular, she steals the chi-gong ball from Josie to give to Victor Pearson. It appears that she is an enemy but it is later revealed that she is an "Observer". An "Observer" is a person from the future who is charged with making sure, with minimal interference, that the timeline undergoes its proper course.
In the series finale she takes Josie's place in the alternate time line in order to save the future . It is unclear if Lucas was able to save the clone from her terrible fate although it's highly unlikely since there is no vortex which allows travel anymore.