A long time ago, I had to give away a pet to protect it. It only took one instance of abuse and I did the right thing. I did right by the cat, and made sure the issues behind what happened were addressed. Not easy all the way around.
To answer your question, Yes. When my wife and I first started dating, and then were married, we spent a lot of time at her place in another country (due to her job being down there or split with her later job near our home). My little dog was being well fed, but I did not have time to play with her as all dogs need. So I asked around and found someone who would love her and care for her. So I gave her to them. They walk her every day, and there is another dog for her to play with, so she is happier.
She was a pound rescue. Very sweet one too.