Within the limits of Catholic "orthodoxy" what is encouraged by most is a strong and active hope that all will be saved.
I take this to mean that it is perceived that there is a possibility that this is the case and it is approved to believe in this possibility.
To some, such a change in perspective may seem to be merely another example of modernity's relentless dilution of the gospel, a superficial optimism that refuses to acknowledge the power of evil in our world and our responsibility for it. In fact an ancient Christian instinct or sensibility for the power of divine grace, precisely in the face of the grim reality of human evil, lies at the hear of this "new" attitude.
John gives the examples of Clement of Alexandria, Origen, and two of the Cappadocian fathers and indicates there are others. He says that
According to Clement, God's absolute goodness implies that punishment can only have a pedagogical, purifying, and healing function, not only in this life, but after death as well. God does not take vengeance, for that would be simply to return evil for evil. But in loving providence God "chastens with a view to the good" of all, much as a father or teacher disciplines a child.
With regard to Origen, according to Wikipedia, though he has been considered through the ages to have been a proponent of this, recent analysis of his extant writings are not conclusive. Nonetheless, John shows that Origen wrote much that provides support for this outlook. I suppose he was wrestling with the cruelty of everlasting punishment and his views evolved over his lifetime and that assuming a consistency of thought on his part does not capture the situation. How did Origen engage the usual passages regarding punishment of Hell's fire? According to John:
Can such a fire really burn eternally? The answer to this question is of central importance for understanding Origen on the subject of apocatastasis. A number of different perspectives emerge in his thought. First, simply with respect to the word and concept of the eternal, Origen often notes the ambiguity of the word "eternal," pointing out that aiôn and aiönios can mean duration without end or simply a very long period of time, an "age" or an "aeon," which would have an end.
This is a topic I come back to from time to time. That's it for now.