When birds lose their tail feathers to unfriendly cats do they regrow them?

I can't quote an individual website to provide a definitive answer, but I have visited several. The answer is 'probably'. Healthy birds will regrow feathers, but there are times that they do not.

Feathers grow from follicles like our hair does, but those follicles can become damaged - either due to poor vitamin intake or due to physical damage. If the cat damaged the follicle, the feather may not regrow.

Also, growing new feathers requires a lot of energy and the bird needs to be in physically good shape to grow them. If the bird is not receiving sufficient energy intake from its food (such as may happen in winter) the growth will be delayed until energy intake becomes sufficient.

As the owner of 4 birds, i must say that it really depends on the bird. My goldcheek lost all her tail feathers when she was a baby as a result of crashes on her tail. The follicles were damaged. in the wild, however, a bird's tail feathers are supposed to be lost when grabbed. A budgie i know once lost all of his tail feathers when he was being captured and regrew them perfectly within 2 weeks!!