Urban threads have had a birdcage in their designs BUT exactly where I can give no more details. Hope you find what you want
I didn't see Turquoise's Tweety yet but I saw that today, a birdcage:
Cathie
http://www.threadbanger.com/post/...
https://www.stitcherymall.com/dis...
http://www.etsy.com/view_listing....
There are at least four done by mops in designs by cuties but you will have to search for them.
I cant find the search box for designs by cuties...do you have to manually go thru each page then? Sorry for being dumb.
I can give you the links, but they are not what you are looking for, no empty cages.