I take it you are referring to them dying on the wing? I have seen a swift fall from the sky dead. But them a swift tends to spend most of its life on the wing- even sleeping on the wing. I would think that most birds close to death would tend not to take off and fly. Most ill birds I have seen tend to skulk in cover.
When I was walking through a park one day , a blackbird dropped dead out of the sky right in front of me.Gave me quite a shock! I've always wondered why you don't see it happen more often.
When my youngest was a toddler in his pushchair, a pigeon fell out of the sky (dead) and landed on his lap. I was more shocked than he was, and before I could remove it, he picked it up and sank his teeth into it. I can remember two women who were passing by stopping to look and one of them said "In my day we used to give them Farleys rusks." It has become a frequently repeated story in the family and strangely, my son is now a vegetarian!