Is there any sin upon one who found a dead pigeon, its wing caught in a waste bin next to the pigeon coop he owns, and what is the expiation for it?

You bear no sin for the death of the pigeon that got caught in the bag you placed, because what you did was permissible, and the pigeon entangled itself. Sin falls upon whoever imprisons an animal and neither feeds nor waters it until it dies, as in the Hadith about the woman who entered Hellfire because of a cat she imprisoned. It is preferable to perform good deeds and give charity.