Crystal stasis

Crystal Stasis (クリスタル停滞) is a state a l'Cie enters upon completing his or her Focus in Final Fantasy XIII and Final Fantasy Type-0. The legend states that the completion of one's Focus and entering crystal stasis grants the l'Cie eternal life.

Datalog
''For l'Cie, successful completion of a Focus holds the promise of eternal life in the peaceful slumber of crystal stasis - or so the legends say. Yet to spend an eternity as an immobile crystal is not so very different from death. The people of Cocoon consequently fear being marked as a l'Cie, equating the fal'Cie's brand with a death sentence.''

Faced with only the choice between eternal damnation as a Cie'th and eternal imprisonment in crystal, it comes as little surprise that many l'Cie decry their fate.

Final Fantasy XIII
When a l'Cie completes a Focus, their body turns to crystal and they become inanimate objects. However, they are not dead, but resting in what some call a "crystal sleep". It is possible to recover from crystal stasis, whereupon the l'Cie comes back to life exactly as they were when they were placed in the stasis. It is unknown how aware a l'Cie is during their crystal sleep.

At the end of the game, Vanille and Fang appear to communicate their thoughts despite being in crystal stasis, however, the dialogue is only heard by the player. L'Cie who are in crystal stasis, may "dream" of things that they cherish. This occurs when both Serah and Dajh were talking to each other, about to meet with the group at the end of the game. Dajh says that "there were a lot of chocobos", alluding to what he might have "dreamed" while in crystal stasis. The legend that completing one's Focus, and being encased in crystal, grants eternal life, originates from the fact that a fal'Cie can call its l'Cie back from crystal stasis to give its servant a new Focus. This way, as long as a l'Cie keeps completing his or her Focus, they can enter crystal stasis multiple times and be revived to live again once their fal'Cie needs their assistance. However, this only leads to a life in slavery under the fal'Cie master.

During the game, it is demonstrated that completing a fal'Cie-given Focus is not the only way to enter crystal stasis: the Pulse legends state that the Goddess stopped Ragnarok during the War of Transgression by placing the Ragnarok l'Cie in crystal stasis prematurely. How accurate the legend is, is up to player interpretation. Cid Raines can also be observed to enter crystal stasis despite having outright defied his Focus.

It appears that the l'Cie may have the power to overcome their fal'Cie-given Focus and give themselves a new one. Whether or not entering crystal stasis was done on Cid's own accord or not, his fal'Cie is still able to revive him from the stasis and give him a new Focus. The case with Vanille and Fang is less clear; their fal'Cie, Anima, did not revive the pair from their crystal sleep for 500 years, and it is unclear whether they were revived by natural methods (the effect of crystal stasis simply running out on its own due time), or if they were taken out of their crystal sleep by an outside force.

At the end of the game, the entire party, as well as the world of Cocoon, crystallize. Apparently due to a prompt from Vanille, Lightning and her friends come out of crystal stasis almost immediately after having been placed in it. It is unknown how Vanille has the power to release the others from the stasis, although it might have been Ragnarok's doing. Serah and Dajh also are released from their crystal sleep and are reunited with the party. Fang and Vanille, however, stay in crystal stasis, perhaps indefinitely. The game's strategy guide appears to suggest that Fang and Vanille did not come out of crystal stasis like the rest because they crystallized themselves willingly.

Final Fantasy Type-0
In Oriense, the exact nature of crystal stasis and Foci is left somewhat vague, but it seems that l'Cie crystallize when they die or when they complete their Focus.

In the game's end, childhood friends Machina Kunagiri, a Byakko l'Cie, and Rem Tokimiya, a Suzaku l'Cie, battle each other. Rem is killed when Machina accidentally impales her on his rapier. While their crystallization is never shown, the two are later found by Class Zero in crystal stasis, with Rem in Machina's arms. Arecia Al-Rashia eventually comes to their crystal and revives them, although it is not explained how she did it.

Qun'mi, a Byakko l'Cie, is crystallized after she willingly relinquishes her l'Cie power to Machina. Zhuyu and Nimbus also enter crystal stasis at some point. Caetuna also crystallizes after summoning the Eidolon Alexander to defeat the Milites Empire, with the assumption that was her Focus. For unknown reasons, her crystal later shatters.

Final Fantasy XIII

 * Men in crystal stasis are crystallized with their eyes open, as opposed to women being crystallized with their eyes closed.
 * Pulse l'Cie are nude while in crystal stasis, but they regain their clothing upon awakening.
 * Dajh is simply encased in crystal, and keeps his clothing. This may be due to him being a child, which the developers would not wish to portray nude, although it is also possible that the manner of crystallization depends on which fal'Cie the l'Cie was branded by.
 * It should be noted, though, that Dajh's Crystal Stasis concept art appears to depict him nude, just like the others. This may indicate that this was changed before they made the 3D model, though whether it was because of Dajh's age or not is still not clear.
 * When l'Cie enter crystal stasis, they glow blue. However, when l'Cie awaken from crystal stasis, they seem to glow a red-orange color.