where do birds suddenly disappear?

Just a random thought...you know how the early mornings and as the dusk falls flocks of birds throng near the trees and the skies are laced in a swirling mesh of black silhouettes. Clearly there must be a lot of flying feathered friends around, not that I've tried ennumerating them. Yet I've only seen one bird carcass in my entire life. It wasn't a roadkill, meaning it was not squished into a two-dimensional sheet of meat, so I guess it counted. Which brings to me the question, where are all the bird carcasses that I should be seeing in the multitudes, although that would be somewhat like a scene from a horror movie. Do the birds, sensing impending death from old age, travel to some final resting place, far from the gazes of human eyes? It's almost unnerving how they seem to disappear without a trace, nary a feather left behind.