Detective Hoffman (Costas Mandylor) is placed in a room with Eric Matthews (Donnie Wahlberg) and Jigsaw middleman Art (Justin Louis), who all have intricate death instruments attached to them. When Officer Rigg (Lyriq Bent) makes it into the room before time expires, he triggers the trap that kills Matthews by crushing his skull, but not before Matthews fires a single shot into Rigg's chest. Art plays a tape, which has Jigsaw's (Tobin Bell's) voice explaining that the purpose of this movie's game was to test his obsession. As his obsession led to the deaths of all those he tried to save, he failed, and he shoots Art in the head before Art can release himself. Hoffman unties himself and gets up, revealing that he is the new Jigsaw, as was revealed by discussion earlier in the film.
Now this is the confusing part:
Even though there is an FBI investigation going on at the same time as these events, it is important to understand that the events of SAW IV take place at the same time as the events of SAW III.
That's why when FBI agent Strahm (Scott Paterson) breaks into the room with Jeff in it (from III) and kills him, Jigsaw's dead body is there. The tape played at the beginning of the movie is removed AFTER everything has happened, so that Hoffman can continue Jigsaw's work with little police interference. It turns out Hoffman was in on Jigsaw's plan from part III as well. Amanda (Shawnee Smith) knew Hoffman was apprenticing with Jigsaw as well, so everything was in place long ago. As for how exactly Jigsaw got a hold of Hoffman and inspired him to follow in his footsteps...well, we'll find out in SAW V, won't we?