Saw IV

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A wax-coated microcassette is found in John Kramer's stomach during his autopsy. It reveals to Mark Hoffman, the detective called in to hear it, that the games, including his own, will continue. Elsewhere, two men - one with his eyes sewn shut, the other with his mouth sewn shut - awaken in a mausoleum, chained at the neck to a winch. The blinded man panics and activates the winch while attacking the muted man, who kills him and removes a key from his collar to free himself.
Four days after Allison Kerry's death, a SWAT team led by Hoffman and Lieutenant Rigg finds her body, and Hoffman warns Rigg for breaking through an unsecured door to reach her. The scene is also investigated by Peter Strahm and Lindsey Perez, Kerry's FBI contacts, who received a message and a key from her. Noting Kramer's and Amanda Young's physical limitations, Strahm states they are looking for an unidentified accomplice; he soon becomes suspicious of Rigg, who has developed an obsession with saving people in the six months since the disappearance of Eric Matthews. That night, Rigg is attacked in his home; he awakens to learn that Matthews is alive and has ninety minutes to save himself, with Hoffman's life also at risk. Meanwhile, he must play his own game to face and overcome his obsession. The detectives are shown to be at each end of a large seesaw: Matthews is held atop an ice block by a chain-noose, and Hoffman is strapped to a chair with electrodes at his feet. If Matthews slips or too much ice melts, both men will die. A man later arrives to oversee the game.
Rigg finds a pimp, Brenda, bound to a chair in his living room. He is implored to leave her, but he accidentally starts the trap by removing her gag, which slowly tears her scalp. He frees her, but kills her in self-defense when she attacks with a knife, having been manipulated into doing so. He is then led to a motel and instructed to abduct the owner, Ivan Landsness, and put him in a prearranged trap in one of the rooms. After finding evidence that Landsness is a serial rapist, Rigg forces him into the trap and leaves after handing him two controllers; he must blind his eyes with blades, but blinds only one eye before the timer expires and the trap dismembers him. Rigg then enters a school where he once assaulted a man named Rex, who was accused of domestic violence. He and his wife, Morgan, are locked in a harness and impaled by spikes, which passed through vital points in his body but non-vital points of hers. By the time Rigg finds them, Morgan has removed all but one spike and passed out from shock. She awakens, and Rigg gives her the harness key and tells her to free herself. He finds the location of his final test and pulls the fire alarm as he leaves.
The agents alternate between investigating the scenes and questioning Jill Tuck, Kramer's ex-wife. She reveals Kramer's work with civil engineering and property development, and that she was pregnant with their son, Gideon, but miscarried after seven months when Cecil Adams, an addict, slammed a door into her stomach while robbing her health clinic. At the motel, the agents learn that the room was rented out to a lawyer named Art Blank, who vanished two weeks prior. Blank, the survivor of the mausoleum trap, is revealed to be the man overseeing the game when he stops Matthews's attempts at jumping and gives him a gun. At the school, the agents learn that all three victims, as well as Jill, were Blank's clients. They find a puppet and a tape recorder in another room, which plays a cryptic message for Perez before its face explodes, sending shrapnel into her face. After Perez is hospitalized, Strahm furiously questions Jill, now convinced of Blank's involvement, and learns that Kramer ended his work with Blank in the wake of his depression, and that Cecil became the first victim of his "games". He connects her story and a prior clue to the Gideon Meatpacking Plant, the location of Rigg's final test.
Strahm arrives after Rigg, but ends up following Jeff Denlon. He finds the sickroom and unlocks it with Kerry's key, and shoots Jeff in self-defense when Jeff pulls a gun on him and demands his daughter back. Meanwhile, Blank pulls out a device which will free them when the timer expires; if used before then, a pair of pincers will sever his spine. Rigg finds them and is shot by Matthews as he breaks into the room, releasing two overhead ice blocks which swing down and crush Matthews's head, killing him. Rigg shoots and kills Blank, believing him responsible for the game, and learns from Blank's tape recorder that his interference caused Matthews's death. Hoffman, the actual accomplice, releases himself from the chair and leaves Rigg to bleed to death. He seals Strahm in the sickroom before leaving the plant. The scene then cuts to Hoffman at the morgue.

Question: Whose disappearance led to Lt. Rigg's obsession with saving people?
Answer: Eric Matthews