Odd that you are talking about lost dogs. A poor dog showed up a couple of weeks ago so frightened she wouldn't let me within twenty feet of me. She slunk away. I fed her, and she was a little less fearful. One day I waved half of my steak in the air. The hungry dog could smell it, and she wanted to eat it in the worst way, but she was afraid. She ran a few feet, stopped cringed on the ground, ran ahead, cringed and ran back. A good illustration of approach-avoidance. Two days ago, she licked my hand, and yesterday, she let me pet me once. Maybe we are like dogs.
I like "you are lost no more. You belong with us." Thank goodness.