The cat I use as an icon lives no more.
He wasn't my child; that would deny his felinity. The death of a child would hurt quite differently.
But he was a member of my household and of my immediate family for 16 years, and he is leaving a cat-shaped hole in my life and my heart, and that of my husband. The other cat seems to miss him too.
He essentially died of old age, although we helped the process along when it was clear there was only suffering left. In retrospect, it is awful how little of life, of his joys, of his places and activities was left to him in the last months before his death, although he seemed to still be appreciating the little he had left until very shortly before the end. Thus, I do not grieve his death at the very end so much as the loss of the cat he once was, and the loss of hope that he would get better (slim as it was).
He used to be a very temperamental and active cat; scared of the vacuum and the outside of the flat, but standing up to and battling cats twice his size (and winning by being more spirited, too). He used to try any food offered to him, and we used to joke that his true name was food, in good times. Also in good times, you never had to dangle a string or throw a ball for long, he would be galloping after it or jumping on it all fours at once. He loved scritches and petting up until the very end.
He was sent to sleep, after 2 days of not eating or drinking (and refusing even water dribbled into his mouth), and I think also not really sleeping, when he became too weak to walk but still felt the need to wander around, while being held on the arm of my husband, and me petting him. I hope his last sensations were of the pains finally going away, and his household (including his feline companion) being there for him.