This is not always possible, but it IS important to do your best.
I am remembering a few years back an old pony at the lesson barn dropped dead in his stall overnight. This isn't a tragedy...Mickey Mouse was, based off of his history, 48 years old and believed to be the oldest living equine in the state of Maryland. It was his time.
The mare who had been stalled next to him for a few years demonstrated behavior that was quite interesting. She would seem fine, then she would look at his empty stall and just WILT. It was honestly like she kept thinking of something she wanted to say to her friend, looked over, and remembered all over again that he was gone.
I don't want to anthropomorphize, but I could see nothing in her other than grief for her friend. She did get over it, although horses have good memories and I suspect she remembered him for the rest of her life.