Birds are monitored by putting a ring on their leg. The ring can then be used to identify the bird if it’s captured or seen with a telescope/binoculars/camera by someone else, or if their carcass is found. Typically it’s just a small metal ring but these days multiple colored rings can also be used, those are put into a public database that anyone can use to identify the bird and see where it has been spotted, when it was ringed, how old it is etc.
A case from few years ago in Finland where cows had to be put down because great tits demolished their udders by pecking for fat. Link.