Time Paradox

Because Metal Gear Solid 3: Snake Eater is a prequel to the other games in the Metal Gear Solid series, there are certain events that would damage the continuity of the Metal Gear timeline, This causes a Time Paradox.

Snake
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 you select Exit instead of Continue) "SNAKE IS DEAD" changes to "TIME PARADOX". This is because Naked Snake is revealed at the end of the game to be Big Boss, the genetic father of Solid Snake, Liquid Snake and Solidus Snake, and if he was to die, the events of Portable Ops, Metal Gear, Metal Gear 2, Metal Gear Solid, Sons of Liberty and Guns of the Patriots could not take place.

Sokolov
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, and he would not be able to complete the Shagohod.

Ocelot
Ocelot can be killed if Snake shoots his unconscious body near the end of the Virtuous Mission, bringing up the Game Over screen and the message "OCELOT IS DEAD". Like Snake, Ocelot causes a Time Paradox because of his involvement in future games. Throughout the rest of the game, he also plays a major role; he switches the Philosophers' Legacy microfilm for a fake and is responsible for the loss of Snake's right eye. Ocelot is also one of the founding members of the Patriots.

EVA
If EVA is killed, a Time Paradox is created, bringing up the message "EVA IS DEAD". Although it is not obvious at tht time, EVA plays a very important role in later events. She was important in stealing the Philosophers' Legacy as The Boss used her to give it to Snake, and was also a founding member of the Patriots. In addition, EVA was actually the surrogate mother to Solid and Liquid, and serves a part in Guns of the Patriots, going by the codename of Big Mama.