Agent Finn was one of two Agents (the other being Jones) who retrieved Emma Pearson, a young girl who seemed to be awakening from the Matrix, and supposedly took her to a clinic to be healed from her "delusions".
Emma once saw her uncle change into something else and this event shook her enough to start questioning her reality and perceive some glimpses of the real world. This, however, lead to the girl being labelled unstable and treated for suspected mental issues. Emma eventually landed in the hands of mysterious Dr. Frey, who asked her several pointed questions up to and including "Have you ever heard of something called the Matrix?" Frey seemed to quickly take an interest in Emma's case and recommended her to be treated at a specialised clinic that he would personally escort her to and oversee the whole procedure.
When the time came, however, Dr. Frey failed to arrive and instead Finn and Jones showed up, claiming Frey had been "delayed" and they were there to escort Emma in his stead. As much as Emma cried and protested, Finn and Jones promptly produced the appropriate paperwork empowering them to handle Emma's case, and Emma's mother and her psychiatrist hesitantly allowed the Agents to take her. Finn and Jones finally assured Emma that she would "be with doctor Frey soon," before leading her away.