There are two magic elements sealed in Rose's choker. One is to open the Signet of this city, and the other is... immortality. A Wingly, Disc 4: Spring Breath Town Ulara
To fulfill her mission, Rose had her own time stopped 11,000 years ago with a magic spell of the remaining Winglies who have stood by her side since. The choker containing the spell isn't visible in-game or in official art, though Rose takes it off twice during the game. A Wingly who has been with Rose from the start states that she has saved the world "at least 107 times"; the Moon Child is born every 108 years, so that information provides a minimum threshold for Rose's age.
When spoken to, one of the Wingly NPCs in Ulara points out that the spell of eternity indeed creates an immortal body, but that it also "corrodes the heart". I don't think he means Rose specifically, as although it's not clear whether Winglies naturally have a long lifespan or whether they all keep themselves alive with the spell, it's implied to be the latter (at least as far as the Winglies in Ulara are concerned), considering that the NPC in question invites the party – as in, any guests, Human or otherwise – to have a drink so as to heal that corroded heart.
"Corroded" here means to be gradually consumed, destroyed – deteriorating. And if you look back at the way Rose is characterized throughout the first half of the game, you'll understand. Rose repressed all her emotions a long time ago, partly because she has lived for a tremendously long time, partly because she has been tasked with an inhuman mission for the sake of a world where no one from her past is left. Whether or not she feels survivor's guilt, it must be overshadowed by the immense guilt (however dulled she became as self-preservation) she feels from all the killing she has done – the slaying of newborns in particular. The combination of the twofold burden may have made her stop feeling human or alive altogether, and the hatred and curses of the people that she takes upon herself may well have led to self-loathing and self-deprivation of any positive elements in her life. At one point, she even flat-out says that she doesn't remember how to smile.
Rose has grown cynical and jaded, and though the story doesn't state how she spent the last 11,000 years, from the way she interacts (and later on develops) around the group, it's safe to assume she hasn't been close to anyone for a long, long time, which may just be why she is such an emotionally distant person, and why she can be quite tactless at times. The trace time has left on her is always present, and is even noticeable in minor things like there being very little that catches her off-guard, her kill or be killed attitude (after all, that's what she's been doing all this time), the way Haschel and Luanna (an NPC in Mille Seseau) notice the pain she keeps wrapped within even when they don't know her story, or her reaction to Lavitz after he says he'll use his new Dragoon power for justice: "[Use for justice? Huh!]"
When the ghost of Shirley appears and challenges the party (consisting of Dart, Lavitz and Rose at the time) to see whether they are worthy of their Dragoon Spirits, she asks Dart and Lavitz questions that can be answered in two very different ways to reflect their values. Of course, she doesn't try Rose, but the thing of interest here is her question:
Lastly Rose, I ask you. What does life mean to you?
Rose needn't prove her worth as a Dragoon because Shirley remembers her former comrade, but what truly sets Rose apart here are her two answers. In contrast to Dart and Lavitz' trials, where the wrong answer keeps you from advancing, neither of Rose's are the wrong choice, as Shirley's response is the same regardless of the player's input: "I've never thought about it." and "Nothing but sacrifice." – evidently, it's all the same to Rose.
None of this, however, is to be confused with Rose becoming corrupted, for if there's one thing that Rose still holds on to, it's her devotion to her mission and the conviction that what she's doing is right. After all this time, after shouldering all the burden by herself, after being called monster, demon and what else, bearing the hatred of all the people, Rose remains selfless, however misunderstood. I think this is best reflected in the several trials (or lack thereof) – including the one mentioned above – that Rose undergoes at different points of the game, which I'll address later on.
The world is created so that it can perish at any time. The creator Soa can recreate one anytime. But, the people living there can accept it, believing it is "fate", or struggle against it. I struggled in order to protect this world that was taken back by friends who gave up their lives. Rose, Disc 4: Spring Breath Town Ulara
Rose keeps staining her hands with blood, fighting to save a world that abhors her – and though that sacrifice gradually strips her of her very humanity, it is perhaps that single-minded devotion that is Rose's defining feature as we see her for the most part of the game. 11,000 years ago, she vowed to put an end to the status quo and fought in a war to give birth to a new future; 11,000 years of loneliness, pain and guilt later, that loyalty to the cause still remains – or perhaps it's more so the loyalty to her former comrades, the wish to at least preserve what they all held dear as the sole survivor, or both.