This is a serious question and not just an off the wall thought. Our cat was dying and wasn't washing regularly. I became unually allergic and needed antihistamines for the first time in my life. The day before the cat died, a white wedding dove arrived in our garden and has 'adopted' us, perching on our balcony and staying with us is a very tame manner. This alone is simply a 'poetic coincidence'.
My wife related this story to a friend who quickly replied that the same ting had happened to her with collar doves when her dog died.
I am wondering whether there is a deep seated smell response in doves that attract them to the scent of a dying animal. I know they're not carnivorous. If this were the case, the ancient association of doves and death may make more sense.
I am aware that this sounds as though its's coming from someone who might have claimed to be abducted by aliens a few times too often, but the behaviour in BOTH cases is totally 'unnatural' and particularly bonding.
I also know that doves don't circle dead animals like vultures. So there may be more coincidence than causality.