Did you play the dystopian soviet nightmare Papers, Please and think “this is good, but I bet it would be better if I was accepting or rejecting cute pets instead of these dreary Eastern Bloc sad sacks.” If so, you're a lunatic. But, the good news is some other lunatic went ahead and made that game.
Animal Inspector casts you as bureaucratic cog in a machine that eats adorable pets. The government has decided there are entirely too many fluffy little animals and it's time to start getting rid of them by way of committee. You join up to make sure you're in a position to save your own loyal canine when the time comes and things get weird from there. You have quotas to hit and unlike shifting through the work visas and forged passports of Papers, Please, the criteria for accepting or rejecting pets in Animal Inspector are often arbitrary or nonsensical. How exactly are you suppose to gauge the utility of a house cat anyway?
Animal Inspector is available for pay what you want on itch.io. I'd recommend you give it a go. I only played for about 10 minutes but could already see things going in a weird direction. I have a feeling this is one of those games with more layers than you might think.