why does the scarf shrink when i rotate the bone
and how do i fix this
Because of two reasons:
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Because it has weights to an additional bone that you’re not rotating.
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Because you do not have volume preservation enabled in the armature modifier.
Of those two reasons, the first is important, and the second isn’t. I’m just including the second reason to be complete. If you solve the first problem but not the second, you’ll get deformation that you want; if you solve the second problem but not the first, you won’t.