Jeff Thomas has a history of depression and attempted to commit suicide on multiple occasions. Jigsaw decided to use his own version of "therapy" to break Jeff of this behavior. Detective David Tapp and Detective Steven Sing were able to rescue Jeff before his trap claimed his life. In the process, Detective Sing was killed by a shotgun trap triggered by a tripwire.
Distraught by the loss of his partner, Detective Tapp grilled Jeff for hours, looking for information about the Jigsaw killer. For days after, Jeff would continually be harassed and hounded by Tapp in the detective's obsession in capturing the killer. So much so, that Jeff contemplated suicide as the solution to his problems. Knowing this, Jigsaw decided to kidnap Jeff again. This time, Jigsaw was determined to finish what they had started.
Again, Jeff is rescued by David Tapp. Scared and angry, Jeff runs away. It is assumed that he survives.