It's dependant on the ancillary itself, and nothing else. Some can be traded, but most can't.
Other than a very few humans, like the tutor, most tradeable "ancillaries" are inanimate things like religious relics.
I wish more ancillary characters could be traded, but I suppose that would make them practically immortal, since you could trade them from one generation to the next, forever. That wouldn't be very realistic.
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