Yeah, Grim does take them, but only when their number is up. I bought two chicks, one grew into a hen, then 2 or 3 days later, the other one finally did, too. So, you can stagger buying them, but that's also not a guarantee.
He'll come and collect your horses, llama, cows, wife, husband, children, parents and more, when their number is up; their time on this Earth has elapsed; it is time to shed their mortal coil.
Death is actually neutral. It's job is to take beings with no preferential treatment. So, he's just doing his job.
Also, feed them vitality treat, I believe it's called. That prolongs their lives. 😉