I think except for the food insecurity and disease from lack of vaccinations, I think stray dogs are probably pretty happy.
Hanging out with their friends all day, getting to have sex, scavenging for food (they still love to do that even when they are well-fed house dogs), getting to eat table scraps— that's the dog's preferred life. We keep them cooped up at home, leave them alone when we go to work or school or anywhere dogs aren't allowed. We treat them like dogs— they get bland food, cut off their balls and de-uterize them. Meh. We "save" them by taking all the joy of life away from them.
I bet the Sochi dogs are having a great time, meeting new people, getting all kinds of delicious, abundant food while so many people are in town. They're living the life.