Death and the Penguin by Andrey Kurkov.
Translated from the original Russian, this noir-ish novel did indeed have death, though mostly off-page, since our hero, Viktor Zolotaryov, is (wait for it!) an obituary writer. It also most certainly had a penguin, named Misha, who lives with Viktor in a rather depressing apartment where he (Misha) mostly stands in corners unless lured out with frozen fish.
There's also another Misha, who may or may not be Russian mafia, who asks for special order obits for people who seem to die soon after, and Misha's daughter, Sonya, who wants to see the penguin, and a militiaman named Sergey Fischbein-Stepanenko, and an elderly penguinologist named Pidpaly. Not all of them meet, but they all swirl around Viktor who tends to go along with the tide. And then, gradually, the tide turns.
Such a strange and wonderful book. I loved Misha the penguin, standing in the shadows and making the best of post-zoo life. And Viktor, well. Viktor, like Misha, is just trying to get along under very difficult circumstances. I was rooting for Viktor. He never did quite what I thought he would do, but I certainly understood why he did what he did.
Beautifully written, but did I mention strange? Very strange. I loved it. I hope you do too.