Animals and nature around us are a reflection of what is happening around us. Sometimes they mirror the internal state of their human. If a dog gets lost, the dog might be reflecting the same behavior and believes their owner is lost too. Case by case, one needs to understand and listen to the dog. Permit yourself to interact with them.
Sometimes the pets dont want to be found. They stay connected without physical contact with their owners. A few times dogs leave homes to give the family a new direction of thought. They come to us as higher forms of messengers. Dogs recognize when something in the house needs to be diffused. Searching for a dog will pave the way to search for something that is missing in our life.