I had baits put in my house by an exterminator and they said it wasn't a worry about my dogs and cats. They used warfarin-type baits and it wouldn't have hurt them if they'd found a dead one and had a nibble. They also said they didn't usually die out in the open, but in their hidey-holes. I wasn't too bothered because my animals are spoilt, they do not need to eat carrion and probably wouldn't be interested anyway. Also, as it's dose-related, they'd have to gobble down lots and lots and lots of dead critters to get in any way enough "stuff' in them to hurt them. From memory, they had different things to use where there were animals and where there weren't. Arsenic or strychnine or anything like that would be more of a worry.
With the chickens, they are so little, it wouldn't take much for them to be affected by anything compared to my dog who has a bit of meat on her bones. And they are complete gutses. If there as a dead anything, they'd eat it, for sure.....
Warfarin itself is tasteless but it's the flavour additives that can make these baits attractive to your dog or cat.