Both are true. Our current dog came to us from a dog hoarder and was 30 lbs underweight, had numerous sever health issues, and I was truthful to DS about where he came from and how he was treated. The dog before that was beaten and afraid of everything and I was truthful to DS about that. The dog before that had been tied to a chain for 8 years and basically ignored, and was truthful to DS about that. If we got a foster who came from somebody who was actually nice to it, but just couldn't afford food or had to go into assisted living, we would tell DS that.
I didn't suggest that OP is unkind to animals. I simply told her what we tell DS when we get foster dogs. She was considering telling her children that the dog died, and I replied that my experience with dogs and our DS (in this case, those who we foster, not get rid of as OP is doing) is to be honest about the situation. Relax.