The first time I went on a two-week holiday after getting my cat, when I got back, she became super anxious about me leaving. Whenever I left, she would wait near door and meow loudly until I came back. It took a while for her to start to trust that I wouldn't just disappear again when I left.
Edit 1: I have no idea idea why people are voting this down. I'd love for somebody to explain to me what about my comment is causing them to do that.
Edit 2: I guess the word "grieve" is ambiguous, but I understand it in this context to mean "being upset at somebody else's death." Of course cats are upset if somebody they like isn't around, that's what I'm describing happened with my cat. I just doubt it's because they know that somebody died.
Edit 3: I think I might have been wrong, see: https://news.ycombinator.com/item?id=41182137 and https://news.ycombinator.com/item?id=41182236