The chances of success are determined by the relationship of the pleading Sim with the newly deceased, and pure chance.
In The Sims Livin' Large, The Sims 2, and The Sims 4, a living Sim who is on the lot can plead with the Grim Reaper, asking him not to take the newly deceased Sim. His nice side shows when a Sim with a gold or platinum aspiration bar dies of old age, during the animation of a pet's death, or resurrecting kids with the Resurrect-O-Nomitron. His personality is perhaps a reference to the personified Death character in Terry Pratchett's 'Discworld' novels. Unlike most legends of the Grim Reaper, he seems to be a kind being in The Sims series. In The Sims 2 and The Sims 3, the Grim Reaper plays a cameo depending on the method of death and the aspiration level of the Sim in question. However, the Grim Reaper does not come if a Sim dies in a Skydiving Simulator in The Sims: Superstar, if a Toadified Sim is eaten by a dragon in The Sims: Makin' Magic, and if a Sim is eaten by the Cowplant in The Sims 2: University.
Starting with The Sims: Livin' Large, Sims that have died are visited by the anthropomorphic personification of death in the form of the Grim Reaper.