Alright, so here are a few questions that've been bothering me for a while. What exactly is a Soul Crystal(/Job Crystal)? How does it work? Can it be stolen? How are more made? How is it "equipped"?
Each job quest in 1.X seemed to come at it slightly differently and give us a different look at how they might function. I'll go through and pull out what bits I can to try and answer those questions. I apologize for the length!!
Fair warning -- each section contains spoilers for its specific quest line.
Black Mage - Hearing Voices
The scene which transpires upon returning to the Ossuary gives us some good clues. We return with the Gem of Shatotto (not yet knowing that it is a BLM soul crystal) and hand it over to Yayake. After Ququruka appears and argues with her, the crystal returns to the player's hand through no direct intervention of any present, implying it cannot be taken from us. However, this might be a specific trait of that crystal. ("The stories tell that only souls blessed by the grace of Nald'thal are granted the keeping of the Gem of Shatotto.")
A quote from Ququruka also implies that unlocking the power of said crystal requires more than simply possessing it, and that there's some sort of acceptance (sentience?) on the part of the crystal. ("You have taken the black, but time is needed before the black takes you─before it permeates your flesh and blood, and every fiber of your being.") This seems to me more than just a lore-appropriate way to address the leveling mechanic.
Paladin - Paladin's Pledge
Here we get some clues as to what constitutes earning a crystal and how they can and can't be received. We are given a soul crystal by Solkzagyl, a disgraced Sultansworn. Upon returning to Jenlyns the crystal is taken from us and replaced with a new one. ("Give me that soul. It is polluted and I must dispose of it. When you come to wield your sword as a paladin, the only soul you may wear is that which is bestowed by a captain of the Sultansworn.") Now, it seems that this is less about the practical workings of the crystals and more about the traditions of the Sultansworn. ("Perhaps an adventurer like yourself finds our rules quaint, even a nuisance in these troubled times. But through reigns long and short, our forebears in the Sultansworn have preserved its rituals and traditions.")
This does, however, beg the question of how Solkzagyl had a crystal to give to you in the first place. According to Jenlyns, it was stolen ("That crystal you bear is indeed the Soul of the Paladin. But it is disgraced, impure. It was stolen from the Sultansworn.") though it's unclear what exactly that entails. Since we later learn that Solkzagyl is an honorable man, it's unlikely that he literally stole a bucket of crystals when he left. It also doesn't seem that he was handing out many, it's implied that after leaving the only one he gives out is to the player. So, either the crystal he gives you was his (we see him acting as a Paladin later, so this would mean he retained his abilities despite losing the crystal. Perhaps because he had already fully "been taken" by the crystal and no longer needed it) OR he was able to create a new one from his own. The latter would explain how new crystals are made in the first place.
Dragoon - Eye of the Dragon
Again as in the Black Mage quest we see here evidence of being chosen by the crystal rather than by the teacher who gives it to us. ("The Soul of the Dragoon I bear glows in your presence─irrefutable proof that you are chosen. What I can ill explain, however, is the why of it.") However, more interestingly, the crystal we are given used to be Alberic's. Though he still carries the crystal on him, he can no longer use its powers, again adding credence to the idea that there's a lot more to it then simply having a crystal in your possession. ("Like Estinien, I once ruled the skies as the Azure Dragoon, although that power has since become lost to me. It was simply by force of habit that I have hitherto kept the soul upon my person.") Later, during Unfading Scars, it is revealed that Alberic lost his powers by sustaining serious injuries in a fight with the dragon Nidhogg. ("As the Azure Dragoon, he met the beast in battle. While he succeeded in repelling it, he sustained grievous injuries that led to the loss of his powers.")
Bard - A Song of Bards and Bowmen
Unfortunately I don't have quest dialogue to quote for this one. You'll just have to trust me. >_>
This quest, like Black Mage's, deals with a soul crystal being taken by one who hasn't earned it. This time it's a by a Qiqirn and your job is to track him down. Again, possessing a stolen crystal doesn't grant the Qiqirn any of its powers. However, this time you have to hunt it down yourself, it doesn't automatically return to Pukno Poki. I suppose it's possible this means that only the BLM crystal can't be taken unfairly, but dialogue with Jehantel upon returning with the stone makes it seem far more likely that the whole thing was a test. It's also possible that, since the crystal was meant for you, nobody else was able to retrieve it.
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The other quests don't offer anything too new, so I'll cover them all briefly:
In the warrior quest we follow the other vein of proving our worth somehow and then being given the crystal by the one who ends up training us through the rest of our levels. Monk does the same, though we do open our Chakra first, it's possible the crystal would have rejected us otherwise. ("This is a soul crystal. It is the mark of my order. Only those in the monkhood may carry it. It is given to novices upon completion of their training. But I have witnessed your transformation. You are ready.") And, lastly, our White Mage crystal is apparently granted to us entirely at the whim of Raya-O-Senna, and has nothing to do with any special qualities of the player being recognized by the crystal itself. ("And, as you act in my name, I hereby permit you the use of white magic. ... [This] is an ancient crystal imbued with the light of succor─by its power, the forbidden art will be yours to wield, albeit within the bounds of your skill as a conjurer.")
This still leaves so many questions unanswered! Discuss! Pretty please?
And thank you to the wonderful people at GamerEscape who have transcribed the quest dialogue for most of the quests I needed information on, thus making my speculations possible.