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The Catholic Church is in substance and essence the same Church that Christ founded and will remain so until the end of time. His Mystical Body, of which He's the head, will continue to be the source of truth and the means of grace for all generations.
Christ assured His doubtful Apostles that He'd protect His divinely established institution. In Matthew 28:18–20 He tells them:
All power is given to me in Heaven and in earth. Going, therefore, teach ye all nations, baptizing them in the name of the Father, and of the Son and of the Holy Ghost. Teaching them to observe all things whatsoever I have commanded you, and behold I am with you all days, even to the consummation of the world.
Our Lord is the reason that truth and grace will never and can never fail universally in the Church. One way Christ preserves the Church He founded was by providing Her with an infallible teaching authority via the Petrine office. He established this papal Magisterium in Matthew 16:18 when He told St. Peter, "Thou art Peter; and upon this rock I will build My Church, and the gates of Hell shall not prevail against it."
The attribute of indefectibility means the Church will never formally teach error on faith and morals, nor will She promote invalid sacraments on a universal level. It doesn't mean, however, that all prudential judgments of the pope or those in authority will be flawless or that local churches, either diocesan or national, will be free from corruption.
The Church has evidenced Her indefectible nature for 2,000 years in withstanding persecutions for three centuries by Roman emperors, two centuries by barbarians and nine centuries by Muslims. The Church's greatest enemies, however, are Her own leaders. Pope Pius VII spoke of these wolves in sheep's clothing when responding to Napoleon's threat of destroying the Church, "If popes, cardinals, bishops and priests have not succeeded in destroying the Church," said Pius VII, "how do you expect to do so?"
Witness the glory Christ bestows on His Bride the Church in Church Militant's Premium show, Majesty of the Faith—The Order of the Church.