If the neck is bent back, there could be various reasons:
Lead, botulism or other poisoning, illness, injury or neurological trauma. The male knows she is in trouble and if she is sick will try to remove her from the habitat. This is nature’s way of preventing the spread of illness in the environment.
You will need many kayaks or boats to gently surround her and herd onto land or slowly enclose her between the boats/kayaks to capture her. There is great urgency to this capture so that whatever is wrong can be quickly diagnosed and treated. The Regal Swan