Welcome Arnold and it's a good question with many possible responses.
Traditional Jewish teaching is that the Prophets of the Tanach are prophecies that relate to each and every generation. So how the words apply to a given generation, hundreds or thousands of years ago, would be different from our lifetime.
But in the current context, if you look from the beginning of the chapter, it appears to be addressing the Holocaust and the massacre of the Jewish people by the Nazis. The remnant are those who physically survive that process.
In various Jewish writings, like Sefer Avkat Rochel of Rabbeinu Makir ben Abba Mori, book 1, sign 1-4, it refers to this time period, which is the beginning of the process of the final redemption as the Pekidah which is alluded to in Isaiah 10:3 and also 10:12. For whatever reason (something we cannot truly understand), G-d's wisdom decreed that it would begin in this way.
There are some who wish to relate this to the Jewish concept of Reward and Punishment for the nation of Israel, but there is another traditional view in Judaism that this decree, which seems to be directed toward the Jewish people, transcends that system and is simply something G-d required according to His wisdom, which is not like our wisdom, as part of the final redemption. That it is really more of an assessment of how the nations of the world relate to the Jewish people, who G-d loves and cherishes, not a measure of the merit of the Jewish people themselves. This association to the re-establishment of the Monarchy of the House of David is alluded to in Isaiah 10:5 and also 10:24 which mentions the rod and staff, which are symbols of the Monarchy of the House of King David.
This time period is also referred to in the Talmud and other places as the Heels of Moshiach, and is a period when the Jewish people suffer greatly.
Concerning your last question, G-d wants all the Jewish people, in every generation, to return to His Torah and to the land which is an allusion to His will. And in fact, that is also G-d's promise through his Prophets. That every Jew will be included in the final redemption because like it says in Isaiah 60:21, they are all righteous in G-d's eyes. And this relates to our belief in the ultimate resurrection of the dead. Not a single Jew will ultimately be left out or forgotten like is found in Tanna D'vei Eliyahu and Pesikta Rabbati and elsewhere discussing when Moshiach ben David accepts his mission from G-d to bring about the final redemption.