Yes, it's very sad when pets go away or die.
My cat was more intelligent and perceptive than most humans I know... She always realized when I was sad, and she would stay with me throughout the day, not leaving my side one minute until she was certain I was feeling better. Just the day before she disappeared, I was feeling sad, so she hid in the house to avoid my parents taking her outside (our cats sleep in the garden, not in the house), then sneaked upstairs to my room and slept on my bed the whole night. And I could give many other examples. She's been with me for nine years, she knew me better than most people do.
And I just realized I'm talking about her in the past tense... which is stupid of me. Like I've already given up. I mean, I don't know for sure she is dead. She could still come back.
Every morning I wake up and hope to find her on our doorstep, as usual. Every evening, before going to sleep myself, I think, "oh, I have to remember to search the house for her" (since she always found finds the oddest places to fall asleep, and then wakes up my parents at 2am demanding to be let out of the house, and my parents don't like that), and then I remember she isn't around any longer. And all the time I think I've seen her out of the corner of my eye, but when I look more carefully, she isn't there.