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Vestiges are Others that are artificially created, often seen as a middle-point between a simulacrum and a ghost and compared to shadows. In other words they are something that can be seen as either a flawed simulacrum, or a ghost that left a deep enough impression in reality that you can use that impression as a mold capable of memories and complex thoughts.
Though this makes them flexible and capable of being molded and altered, they are impermanent. Given time and external pressures they started to degrade and the degradation grows worse over time, to the point that it takes more and more effort and energy to keep them intact. Eventually they break down, but they can be shored up with other spirits and Others to become more Wraith-like.
The book Vestiges: Glimmers and Gasps contains a wealth of information on the subject.
Rose Thorburn created a vestige for her grandson Blake to help him fall into the roll of a practitioner and possibly to secure a heir. Because of this they count as one person as she now serves as his reflection and her voice carries the power to influence Others, as their family line are typically female. Because of their connection she draws power from him. Then it turns out she created Blake as the vestige rather than Rose to act as her protector.
Johannes uses them in his territory as playthings for Others, who wish to return to the days before the Seal of Solomon, at the admission of gaining power from them. He shores them up with mouse and dog spirits to affect the with his implement.
↑Vestiges can arise naturally. In fact, you could make the argument that ghosts are a subset of vestiges as a whole - they're just really reinforced by the ongoing and complicated pattern of life and death, arising from things that push beyond the boundaries of that pattern.
You're otherwise right, though I'll note only some vestiges have a self. Vestiges are essentially the equivalent of tracing existing work, creating mock replicas of some or all of something already in existence, or taking the stuffing out of X and leaving only the husk. They resemble the original but something is missing and they're often very fragile. They're not all alive.
A faerie using glamour and trickery to steal your shadow and create a shadow you would be creating a vestige. A mockery of you shored up by expectation, by spirits, by the fact it's acting like you and getting away with it (the wheel is still spinning but the hamster is long gone). Depending on how that situation played out, the shadow could gain strength enough to become something else while depleting you, and you'd be the vestige instead.
Curses and magical attacks that hit you on a level beyond the physical and the real could also leave you on the brink of... not death, because your heart beats and you breathe, not being emotionally or mentally dead because you think and feel, but being so less that you're barely not there. The effect might be like Bart when he sells his soul or Gollum with the one ring. Practitioners might put too much personal power into a created item or demesne and lose the power to affect the real world, making them very close to being that husk.
Most don't stay in that state for long. It's either the last phase before utter destruction or other things will jump on it or capitalize on it, because a vestige is a pretty valuable resource, a nice home for something parasitic, or a 'stock' that could quintuple in value in a matter of days, as things return to normal.
It's like taxidermied animals, sculptures, or those models of people with the guts and internal organs on display, but its practice that gets them there and practice that keeps them going, playing off of the fact that you can look at them and you can say "that's a human" or "That's clearly Chad", but they're not, there's obviously something missing or gone. - Vestige suff