In the second season finale (The Past is Never Dead), it's revealed that Judith is The Camp Motega Killer and that Wren is actually Owen Turnbull, her son who committed suicide after being framed for Talvinder's murder. The "Wren" shown is simply a figment of Judith's imagination, a hallucination she's using in order to justify her crimes.
Owen "Wren" Turnbull Edit
It's assumed that Judith and Owen had a close mother-and-son relationship before his suicide. As not only did Owen send her letters while he was incarcerated, but his mother actually spiraled into insanity after his death.
During season two, "Wren" and Judith share some questionable moments, which makes you wonder how close their relationship actually was.