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Fearing that your question will be closed as either off-topic or opinioned based, it seems that the only answer one could possible give would be entirely based on speculation.
The Catholic faith could possibly be preserved in one of several ways, like these for example:
That last scenario is not without precedence. It has happened before. The faithful of Japan survived in great numbers for some 250 years without any Catholic priests or missionaries. That is not a little thing!
In 1614, all Catholic missionaries were expelled from Japanese soil. Fr. B. Petitjean arrived in Nagasaki, Japan in August 1864 and was able to construct a small Church. On March 17, 1865 he discovered that the Christian faith had survived in Japan for some 250 years without any missionaries (priests) to administer the sacraments!
Japan was forced to open to foreign interaction by Matthew Perry in 1853. It became possible for foreigners to live in Japan with the Harris Treaty in 1858. Many Christian clergymen were sent from Catholic, Protestant and Orthodox Churches, though proselytizing was still banned. In 1865, some of the Japanese who lived in Urakami village near Nagasaki visited the new Ōura Church which had been built by the Paris Foreign Missions Society (Missions étrangères de Paris) barely a month before. A female member of the group spoke to a French priest, Bernard Thadee Petitjean, and confessed that their families had kept the Kirishitan faith. Those Kirishitan wanted to see the statue of St. Mary with their own eyes, and to confirm that the priest was single and truly came from the pope in Rome. After this interview, many Kirishitan thronged toward Petitjean. He investigated their underground organizations and discovered that they had kept the rite of baptism and the liturgical years without European priests for nearly 250 years. Petitjean’s report surprised the Christian world; Pope Pius IX called it a miracle. - Kirishitan (Wikipeia)
In Japan this is liturgically celebrated as the Finding of the Japanese Christians. Sorry, St Patrick's Day is not a big thing this day in Japan!