I believe they do, it usually happens to peaceful persons in their family. Acient hippy migh be right but, Spirituality does exist! My friends cat died and three days later she saw the cat in her home. The cat thing also happened to my daughter.
I believe this can happen as the person's spirit leaves the body on their way "to the other side" - but they don't come back. If you have a strong connection, they visit you on their way "out" - when you are conscious - not asleep. They cannot enter your subconscious mind. You feel their presence for a brief moment and what you feel is your reaction to their presence. You know what they want - to reach out to you in love and comfort you - and you can dream about the experience. (It's hard to explain)