Last Tuesday, my mother's cat, Chloe, who had been with our family for over 20 years, went out and didn't come back that night. The next day she didn't return either, and after going outside and calling her name around the property, my mother had the feeling she'd gone somewhere to die peacefully.
It wasn't until Sunday morning that my dad found her in a very bad condition, her hind end crushed, dragging herself back to the house.
At the same time, I happened to send my mom an email saying that Fina wanted to see her on Skype, so when she'd gathered herself enough, she called us and let us know what was happening at home.
At one point, my mother asked what the Buddhist perspective was on compassionately ending her suffering. I couldn't say I knew, but the only thing that I could get out was, "let her do her thing."
After talking, I found and emailed her this quote from Thanissaro Bhikkhu in an article titled Educating Compassion;
"...he [Buddha] regarded every moment of life as an opportunity to practice and benefit from the Dharma. It's a well-known principle in all meditation traditions that a moment's insight into the pain of the present is far more beneficial than viewing the present moment with disgust and placing one's hopes on a better future. This principle applies as much at the end of life as it does anywhere in the middle."
I also found these two quotes from the Buddha (not from the same article);