QUESTION: “What happens to animals when they die? Is there any chance of seeing beloved pets again after they pass away?”
ANSWER: I love all kinds of animals and have always been very attached to my pets. I've often asked the same question, especially when I've lost pets in the past. Unfortunately, the Bible is totally silent on the subject, so I can't give any absolute answer. However, based upon what the Bible does teach I myself have some hope of seeing beloved pets again in the new heavens and the new earth that Christ will establish when He returns.
There is no indication in Scripture that animals have souls, certainly not in the same sense in which human beings have souls. Genesis 1 & 2 stress that man was made unique from the rest of the creatures God made. God breathed into man a spiritual nature which was made in the image of God. Rationality, morality, wisdom, etc. are characteristics that we share in common with God and which enable us to have a personal relationship with Him. Because of that image of God in us, we are morally accountable to God.
Animals do not have that same accountability, so sin is not an issue with them. Any evil that we see in the animal kingdom (e.g., brutality) is a result of the sins of man, the effects of the Fall on creation. So there is no reason why God could not "resurrect" animals who die in this life, remove the effects of the Fall, and give them eternal physical life in the new heavens and the new earth as a part of the renewal of all things after Christ returns.
Some of the prophetic passages in Scripture that speak of that renewal in the future speak of the presence of animals. This makes sense, because we don't expect the new heavens and new earth to be totally different from the creation we now know – it will just be perfect and greater in glory. I believe (not based on any particular Scripture passage but based upon my understanding of the character of God and my experience) that God gives us domesticated animals like dogs and cats as a gift of His grace to give us companionship and comfort in a cold, hard world, and to give us a foretaste of the world to come. In light of that, I have no difficulty believing that He may resurrect our most loved pets in that new world, just to give us that joy and pleasure as His dearly loved children. No guarantee, but this would seem very consistent with the nature of the God that I love and worship.