Sugar looks adorable, but I have a chicken who defies definition, too. I would have thought she has a genetic defect, maybe from breeding too closely. Hopefully her other systems work fine, though it sounds like she won't be an egg layer. As long as there is no suffering, then why not have a 'different' bird. Good for you....and always will be a talking point.
Here's my own little mystery...Moel, aged just under 20 weeks....yes you read that right!
Beak, feet, eyes, comb, everything else OK....but what ever happened to her feathers???
She seems otherwise normal, so she's staying. Should be a Blue Partridge Brahma.....not inbred.....parents normal....but head and neck....Blue Partridge Brahma...body Wonky Silkie (no Silkie ever been within miles of our place and bred from out own birds).