I've recently started playing "Shadow of Mordor" (way overdue, I know) and upon my first death I was amazed at the elegant way in which it was handled in the overall game loop.
In most games there is a quite simplistic risk/reward mechanism that relies in player death. In order to keep the player engaged there is a risk - failure leads to restarting a section of the game - which usually can be simplified as player death. The reward is progress and the feeling of accomplishment.
This is a classic mechanism for game design: you can see it on anything from RTSs, where you have to restart the mission, to platformers where you have to redo anything from a specific section, level or even the entire game (for more "old-school" titles) once all the lives run out. You can see this failure - go back - repeat concept in most games you can get your hands on.
Of course, there have been attempts at subverting this. "Wario Land 2" for instance, completely removes player death but still relies on the same formula of failure leading to repetition. It does this in extremely ingenious ways but the end result is still the same. The most notable trope being failure to clear a vertical platform
section will make you fall and have to repeat parts of it, but not too
much - a mechanic which can be seen in titles so disparate as mainstream Mario titles and the Assassin's Creed series.
So-called "open" or "sandbox" games have an easy cop-out of this mechanism. The non-linearity leads to more interesting approaches - enemies may not be there and force you to take a different approach. Bioshock handles player death and failure as a simple consequence, the player is recreated elsewhere, but the world remains as he left it. Yet some players have said this removes some of the challenge - after all, where lies the enjoyment of the game if failure has no consequence? The entire game experience becomes busywork.
Curiously, Roguelikes are an interesting subversion of all this. By some definitions of Roguelike,
the player literally shouldn't have a chance at repeating a section he
has just failed at. Failures are permanent and openly embraced. The fun
is derived from the potential of doing better next time by taking
better choices when faced with similar situations.
There's also other interesting approaches to player failure: "Life Goes On" uses it a mechanic. The remnants (corpses) and consequences of your failures are used to (sometimes literally) build a path towards success.
Coming back to "Shadow of Mordor", every time the player dies - that is, every time he fails - he isn't forced to repeat gameplay sections, he comes back, the world left as it was, but his failure will lead to consequences in the world, usually punishing. The enemy you fought against and failed, is now stronger. It's an ingenious concept: failure isn't rewarding yet isn't punishing in itself. Yet even his failure has changed the world in noticeable ways.