The protagonist can't really ever die. This does not mean the player can not somehow fail their mission completely however, only that it never is directly because of player character's death or incapacitation.
The first video game about Deathless was released in 1992.
Does not imply the protagonist is immortal, only that either there's no chances for them to die, or the game just assumes that the protagonist avoids any fatal injuries.
* No fail state (when it's absolutely impossible to fail)
* Retry points
* Non-lethal - no-one dies by the protagonist's hand
* 1 life
* Unlimited lives (similar concept, differing only with the fact that player character can die, it's just not going to do anything)
* Permanent death