After Simons accident which left him wheelchair bound, Dr Purnell was hired to be Simons therapist to help him cope(normally)with his situation. When they are talking, its clear he does not want to talk about his home, nor school life, as he gets aggressive when Purnell brings up these topics. Because of the lack of success in the therapy sessions, Purnell suggests he try cognitive therapy to write his feelings down instead of just bottling them up. However, the success in this therapy will depend on what the player does.
His fate depends on what the player does, such as not killing carcass and/or not giving him the gun. In ending 1 and 3, Simon goes on to kill Purnell, stating that his therapy either didnt work, but instead made his depression worse, or that his attempts to help Simon were useless. However, on the other side, in ending 2 and 4, Purnell is spared. Simon apologizes to him in E2, stating that "Not everyone can be saved." In E4, Simon is simply admitted to a mental hospital, with Purnell still being his therapist.
ignore the top left corner, best image i could find for this battle
To continue on, you must first get the code to the attic door in which Purnell fleed to. It changes depending on whether or not it is a new game, or a loaded game from the previous days. Once you reach the attic, there will be a ledge with some ammo, a morphine syringe, and a gun. All of these can be needed, but are optional to grab. Once you walk forward a bit, you should be put into a cutscene, after which the battle will start. Its a simple gunfight, but Purnell can be hard to fully finish off if you do not know what you are doing. When the battle is over, Simon will walk over to Purnells dead body, and crush his head in, destroying both his skull and mask. If you did not trust him with the gun, you will be given the Taurus revolver. However, if you do trust him, then upon his death you will be given the Ruger P345.