Sydney had no idea that she was actually a human named Daniel Gibson, Jon's grandfather. As a safety measure, he had wished that whatever form he took, he would still be able to make wishes using the wishing stone. But he hadn't intended on becoming Sydney. He made a wish to be closer to his grandson and in turn the stone turned him into Jon's dog.
So, Jon's grandfather wasn't dead, afterall, but rather was transformed into his dog.
