Death Is a Bitch
When Peter tries to get out of paying a doctors bill by faking his own death, he is visited by Death himself, who wants to take Peter away. After Death twists his ankle while chasing Peter, everyone on Earth becomes immortal while death is incapacitated.
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Family Guy Season 2
Family Guy Episode 6
Lois finds a lump on Peter's breast and worries that the lump could be cancer. Peter sees a doctor. It turns out to be a benign fatty corpuscle, but Peter does not want to pay the hospital bill, so he declares himself deceased on the insurance form. When Death shows up at his house, Peter tries to run away and Death chases him, but falls down and sprains his ankle. Death does not want him to tell that everyone will be immortal until he heals his ankle. But Peter tells and proves that everyone is immortal when he is intoxicated. The fact that no one can die becomes top news.
Peter is forced to take over Death's job in order to prove to people they can still die and is assigned by Death to kill the kids from Dawson's Creek, but refuses to go through with it when he sees other passengers will be affected. Instead, Peter unwittingly kills two airplane pilots, proving people are not immortal, and forcing actress Karen Black to land the plane. Satisfied that Peter has restored the natural order of life and death, Death leaves him be for the time being.