Stigmas are special abilities that are passed down to incarnation by their sponsors - constellations.
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Almost all Stigma's have an interference similar to; a constellation gaining a stigma along with their status; finding an incarnation to sponsor; giving them a trial which rewards them with either a fable or stigma, or even both. Sometimes a constellation may gift an incarnation a stigma in order to persuade them into sponsorship. Other times it may be out of pure will; such as when Kim Dokja was given a trial to overcome his fears and was rewarded one. In Hyunsung's case, it provides us with more information; you may succeed the trial even if you were possessed during said trial. It also implies that Kim Dokja (and others,) may pass on stolen abilities, seeing how Yoosung was able to use Way of the Wind.