score:7
The papacy will last until the end of the world, as the First Vatican Council said in Pastor Γternus (July 18, 1870), ch. II, "On the Perpetuity of the Primacy of blessed Peter in the Roman Pontiffs":
That which the Prince of Shepherds and great Shepherd of the sheep, Jesus Christ our Lord, established in the person of the blessed Apostle Peter to secure the perpetual welfare and lasting good of the Church, must, by the same institution, necessarily remain unceasingly in the Church; which, being founded upon the Rock, will stand firm to the end of the world.
If the papacy "will stand firm to the end of the world," so will Church Militant (the Church on earth), as the papacy without the Church would be an absurdity.
Perhaps a more interesting question would be: "Will there be a pope at the time of the end of the world?" I believe this is still an open question.
Upvote:3
I wish I could find a reference, but I've heard priests say, probably on Relevant Radio, maybe EWTN that the Catholic Church would exist even if there were no members left on Earth.
There is always a chance for renewal, even if we have to crawl back from being one-cell microbes.
God has bound salvation to the sacrament of Baptism, but he himself is not bound by his sacraments.
CCC 1527
If God is not bound by His sacraments, there's always a way to bring the Catholic Church back to full steam as long as there's heat in the Universe (maybe even without heat, who knows).