I had a sister who was stillborn. She would have been named "Mary Burke." And a friend of mine lost a child who would have been her only daughter ("Sky Angel.") So what happens to these souls? According to St. Gregory of Nyssa, the souls of all who die in infancy (baptized and unbaptized) "will advance to that perfection which comes by growth...for God will bring to perfection the soul according to it's nature."
Following Thomas Aquinas, there was the Scholastic theory of Limbus infantum.
And Karl Rahner (the great 20th century Roman Catholic Theologian) theorized that unbaptized infants (who die before making any moral choices) might be re-embodied here on earth. As for baptized infants who die before making any moral choices, Rahner had the interesting idea that upon death, they had an immediate "pan-cosmic" connection to all of creation. And experienced something of all the pain and joy of earthly life, with all it's lessons. And with this background they easily chose heaven, and were received into the beatific vision.
If true this would not mean that our lives here are unnecessary, because they need us here to give them that background. And there will be degrees of glory in heaven (1 Corinthians 15:41.) If a baptized infant dies without making any moral choices here, It dies without original sin. But it also dies without having any personal merit. It enters heaven purely on the merits of Christ. And without a crown. It's degree of glory corresponds to the baseline of grace given it at baptism. An adult who lived a full life here started with a baseline of grace, but through every subsequent act of freewill--every prayer, every loving deed, every trial endured in patience, and every sacrament received--their degree of sanctifying grace grew. The infant experiences God perfectly, but according to a baseline capacity. St. Paul writes in 1 Corinthians 15:41, "Star differs from star in glory." An adult who suffered through the trials of life, resisted temptation, and chose love over selfishness enters heaven with a vastly expanded capacity. But there's no jealousy in heaven. The adults will look upon the children as proof that salvation is ultimately a gift. And the infants will look upon the adult saints with loving admiration--as heroes.
Through the Beatific Vision, all souls in heaven see God, and in seeing God, they see and understand one another perfectly (through God's eyes, as far as they're able.) The adult saints can share their "narratives of victory" with the children, and the children can receive and appreciate that wisdom perfectly (according to their capacity.) There is a deep, eternal exchange of love, where the diverse experiences of Earth weave together into a single, flawless tapestry. Through the Beatific Vision, all souls in heaven see God, and in seeing God, they see and understand one another perfectly. The adult saints can share their "narratives of victory" with the infants, and the infants can receive and appreciate that wisdom perfectly according to their capacity. There is a deep, eternal exchange of love, where the diverse experiences of Earth weave together into a single, flawless tapestry.
And the Church issued this statement in 2007:
It is clear that the traditional teaching on this topic has concentrated on the theory of limbo, understood as a state which includes the souls of infants who die subject to original sin and without baptism, and who, therefore, neither merit the beatific vision, nor yet are subjected to any punishment, because they are not guilty of any personal sin. This theory, elaborated by theologians beginning in the Middle Ages, never entered into the dogmatic definitions of the Magisterium, even if that same Magisterium did at times mention the theory in its ordinary teaching up until the Second Vatican Council. It remains therefore a possible theological hypothesis. The principle that God desires the salvation of all people gives rise to the hope that there is a path to salvation for infants who die without baptism..., and therefore also to the theological desire to find a coherent and logical connection between the diverse affirmations of the Catholic faith...