Hey everyone, first time poster so I'm not familiar with all this, but I wanted to come in and share that I think I've found a solution to the aging problem for chickens, llamas, and cows through a mod.
I've been so frustrated with this bug and did some diving around, where I found a page of Cottage Living mods by someone named Bienchen. (Just search online Bienchen Cottage Living mods and it should be the first result.) They have a mod that slows the aging of chickens/cows/llamas and separate mods to completely stop the aging of rabbits and foxes. But I didn't want my chickens to die at ALL, so I downloaded the cottageanimalslivelonger mod on that page, opened it in Sims 4 Studio (there's two in the zip but it doesn't matter which you use), and edited Line 15 in the code to <T n="decay_rate">0</T>
I saved and applied the mod, and I've tested it for more than 28 in-game days, and the reaper has not come for my elderly chickens. They're still running around as happy as can be. I still get the notice about the reaper each time I load the household, but he never comes. I haven't tested this with llamas and cows, but in theory it should work for them, too. (I think those three animals are categorized the same because they all need a barn/hutch.)
I don't know if this has completely stopped the aging or just significantly slowed it (it should be stopped though, if the number is at 0), but the results seem promising so far. If you try this out, please let me know if it also works with llamas and cows, and also if it only seems to slow the aging and not stop it.