Given that moshiach can come at any time, what will happen to those that are in the process of conversion? Certain passages such as yevamos 24b, geirus would no longer be performed in the messianic era. At the same time there were general limitation on geirus lest people try to join the Jewish people for motives other than wanting to serve Hashem. (such as financial growth or some sort of benefits)... However, Yisro who already had stature and wealth was allowed given that he had "good intentions" and no ulterior motive.
An opinion I read before, source which to my shame have forgotten, stated that ultimately all the world would become Israel. This is a beautiful thought but it's debatable given the prophecies of nations coming to celebrate sukkos.
I think there might be geiros available, post the coming of moshiach, for those truly in love with the Torah and Hashem. I guess we'd all have to live it and see what happens. A convert is compared to a deer among sheep in the Midrash, these people leave families and lives behind just in an effort to be counted among the Jewish people. I don't think such a person would ever be set aside by Hashem. I like to think they would be allowed to finish their geirus. I was hoping for some citations or baraitot to support my thought but your comments help more than you think. Thanks.