Because Metal Gear Solid 3: Snake Eater is a prequel to the other games in the Metal Gear series, there are certain events that would damage the continuity of the Metal Gear timeline. This causes a Time Paradox.
If Naked Snake is killed, the game comes up with the traditional Game Over page displaying "Snake Is Dead." After a little while (or quickly if the player selects Exit instead of Continue) "Snake Is Dead" changes to "Time Paradox." This is because Naked Snake is revealed to be Big Boss at the end of the game, the genetic father of Solid Snake, Liquid Snake and Solidus Snake, and if he were to die, all subsequent events could not take place. The player can access the gadgets menu and select the revival pill to quickly reverse this process so that Snake can stay alive.
A grenade can be thrown through the window of the room Sokolov is being held in, bringing up the Game Over page displaying "Mission Failed." His death compromises the Virtuous Mission, as he would not be able to complete the Shagohod. Sokolov also plays an important role during the San Hieronymo Takeover.
Ocelot can be killed if Snake shoots, stabs, or throws a grenade at his unconscious body near the end of the Virtuous Mission or kills him while he is on the catwalk during the fight with Colonel Volgin, bringing up the Game Over screen and the message "Ocelot Is Dead." As with Snake, Ocelot causes a Time Paradox because of his involvement in future events (such as being the one responsible for the loss of Naked Snake's right eye). Ocelot is also one of the founding members of the Patriots and is the right hand man of Liquid Snake and then Solidus Snake. His death would also impede a future Old Snake from killing Liquid Ocelot in 2014 because he is already "dead."
If EVA is killed, a Time Paradox is created, bringing up the message "EVA Is Dead." Although it is not obvious at that time, EVA plays a very important role in later events. She was a founding member of the Patriots and was actually the surrogate mother to Solid Snake and Liquid Snake, and serves a part in Liquid Ocelot's Insurrection, going by the codename of Big Mama. In terms of events during that time, she was also essential for the completion of Operation Snake Eater, as she was the one who piloted the WIG out from Tselinoyarsk, as well as fighting the Shagohod and escaping Volgin's forces.