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The field group remains on the page when the fields within that group are hidden using Drupals form states or the "Conditional Fields" module, which is just a ui way on implementing form states.
I think we can accomplish this by writing some jQuery code to check if the fields are hidden, or visible. If all fields are hidden then we just can hide that field group. Although, I think we would have to react on when the dependent field has been changed, so we can make the field group visible so the field dependencies are then shown correctly.