Stupid sensitive me started bawling when I opened this thread.
We lost one of our kitties in a similar way. He was not sick though, just very old. He was my mom's first cat, her and my dad bought him together just after they were married. Anyways, Clyde, and our other kitty bonnie were never really close, but we got bonnie when she was a little baby and she grew up with him. As he was dying, he kept trying to get out of the house, so he could go and be by himself, like he didn't want us to see him like that. He used to purr to, I think, reassure himself, but the most amazing thing of all was the way bonnie just laid beside him the entire time. She let us pet clyde when he was awake, but when he was sleeping, or if we tried to pick him up, we'd get smacked with her claws. After Clyde died, mom took him to the vet, and he was cremated. His little box is in my mom's room (strange as that sounds).
I'm sorry about your kitty. It's never easy to lose a pet, especially one that you love so much.