A short spiritual teaching (YouTube video) by Elay Amitay Halevi about the meaning of a pet's death: pets arrive to help humans open their hearts and provide guidance, and when they die their souls have completed their mission and elevate into the human kingdom. The speaker says these souls can return in other forms (guardian angel, friend, an 'ebor' that attaches to and guides a person) and offers a brief prayer to release the pet and accept reunion in a future incarnation.
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What does it mean when the soul of an animal, one that is so close to you in your life, passes away? The sages explain that these souls actually come into your life as a dog or a cat or a pet that is close to you in order to elevate you. They are there to provide some form of guidance and companionship and love. They are there to help you practice opening your heart so that you can do it with your future partner. These animals can communicate with you soul to soul, and they are there to share something with you. But when these souls pass away, you need to know that they have done their job in your life. Their next evolution is to enter into the human kingdom. And although it is sad and although it is painful, you must know that by you releasing them, you are allowing them to come back into your life in a different form, possibly even a closer form. The soul of an animal, then, can elevate to the human kingdom and come back to you in many different ways as a guardian angel, as a friend, or as what the sages say is an ebor, a soul that attaches to yours and guides you emotionally, spiritually, even physically throughout your life. Here's a prayer that you can say. Creator, I accept the passing of my best friend. I allow their soul to elevate to its next incarnation so that I, too, can elevate. And I know with certainty that we will be united again.