What is the biblical support that the Catholic Church is the custodian of truth? The doctrine of papal infallibility is not founded on biblical texts specifically. It is founded on the "biblically supported" doctrine that the church is the custodian of truth. What is the scriptural support for the Catholic church's claim that they are the custodians of truth? What does it mean to be the custodian of truth. Does this mean that they believe in modern revelation and receive direction from God?
The key Biblical passage is Mt 16:18: &quot;And I tell you, you are Peter, and on this rock I will build my church, and the gates of Hades will not prevail against it&quot; (NRSVCE). Though such a citation inevitably hearkens back to certain meta-questions about the use of &quot;πέτρᾳ,&quot; the Catholic Church has always seen it as referring to the specific ministry of Peter, out of which grew the institution of the Papacy.
It would follow as a corollary that this &quot;not prevailing&quot; depends not on any human strength but on a special kind of assistance: hence the &quot;parakletos&quot; referred to most insistently in Christ's Last Supper Discourse.
Important to note (though perhaps a bit ancillary to this particular question) is that a Catholic would take issue with one notion that seems to underlie your question, that a doctrine is valid only insofar as it is &quot;founded&quot; on or directly corroborated by Scripture. Though Scripture is an extremely important &quot;fons revelationis&quot;--and some theologians would be willing to argue that all doctrine can be implicitly found in it--the Catholic Church has always had strong confidence in the value of Sacred Tradition (capital &quot;T&quot;), built on the practice of the Apostles and the teachings of the early Church.
As for the precise meaning of &quot;custodian of the truth&quot;: the Catholic Church speaks of a &quot;depositum fidei&quot; (deposit of faith) closed at the death of St. John, which constitutes the public revelation of Christ, in whom all the truths of salvation are contained. Though further revelations (&quot;private revelations&quot;) are not rejected, and sometimes are approved as useful (such as the apparitions at Fatima and Lourdes), they belong to a separate category altogether because they are directed at understanding the &quot;depositum&quot; in a more profound or culturally focused way. Catholic dogma all exists in the &quot;depositum,&quot; though centuries of development and interpretation prompt us to see things that were not clear before, such as the Assumption or Immaculate Conception. No &quot;modern revelation&quot; that purports to add something to the deposit of faith is admitted by the Church.
The proper relation of Scripture, Tradition, and the Magisterium is expressed well in Dei Verbum, the Dogmatic Constitution on Divine Revelation. Cf. especially #10:

Sacred tradition and Sacred Scripture form one sacred deposit of the word of God, committed to the Church. Holding fast to this deposit the entire holy people united with their shepherds remain always steadfast in the teaching of the Apostles, in the common life, in the breaking of the bread and in prayers (see Acts 2, 42, Greek text), so that holding to, practicing and professing the heritage of the faith, it becomes on the part of the bishops and faithful a single common effort. (7)
But the task of authentically interpreting the word of God, whether written or handed on, (8) has been entrusted exclusively to the living teaching office of the Church, (9) whose authority is exercised in the name of Jesus Christ. This teaching office is not above the word of God, but serves it, teaching only what has been handed on, listening to it devoutly, guarding it scrupulously and explaining it faithfully in accord with a divine commission and with the help of the Holy Spirit, it draws from this one deposit of faith everything which it presents for belief as divinely revealed.
It is clear, therefore, that sacred tradition, Sacred Scripture and the teaching authority of the Church, in accord with God's most wise design, are so linked and joined together that one cannot stand without the others, and that all together and each in its own way under the action of the one Holy Spirit contribute effectively to the salvation of souls. Source: Dogmatic Constitution on Divine Revelation Dei Verbum Solemnly Promulgated by His Holiness Pope Bl. Paul VI, November 18, 1965.