They are not sewn into the tartan, they are part of the weaving, and not an added decoration.If you look closely at the Rampant Lion kilt, you will be able to see that the normal twill weaving is changed into non twill weave for the pleat portions that have the design element on them. The wrong side of the fabric will probably have the reverse elements in the pattern element in the alternative colour to some extent, although with clever weaving this will be disguised a little.
So no loose threads, it's all contained within the actual cloth













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