This is a prevalent issue with any clothes or accessories that encapsulate parts with morph features, typically the face or head. There are multiple ways that you can do it, but these methods are not for beginners and require some experience to implement them.
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Weight painting the bottom part of the cloth to the jawbone instead of the head. If you are using shapekeys or morphs that drive by using keys, then you will have to create an independent morph for such behaviour.
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Adjust your cloth manually in Blender or Maya and then export to create (non-baked) morphs that can be triggered by the morph targets value. The value can be increased or decreased depending on your jaw opening. You can use this method to fix any distorted parts, and it will fix them by adjusting the morph targets slider value.
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Reweighting the whole cloth so that it matches all the facial bones.
As I said, if you have no idea what I’m saying, perhaps you could start taking a look at weight paintings for clothes if not just hire someone with a 3d model experience background. You could easily find it on Fiverr or Freelancer. Cause this topic is quite complex and requires a lot of trial and error to make it look proper.
Or you can just ignore it.
Hope it helps.