The First Vatican Council defined ([*Pastor Æternus* ch. 2][1]) the dogma that there will be a perpetual line of successors of St. Peter, the first pope:

>If, then, any should deny…that blessed Peter should have a perpetual line of successors in the Primacy over the universal Church…: let him be anathema.<hr><sup>Si quis ergo dixerit, non esse … ut beatus Petrus in primatu super universam Ecclesiam habeat perpetuos successores…: anathema sit.</sup>

However, the Church has not defined that there must be a pope when the world ends, so conceivably the end of the world could occur during an interregnum.* Nor has the Church put a limit on the length of an interregnum.

<sup>*In fact, [Antichrist himself will probably be a false pope (antipope)][2].</sup>


  [1]: https://www.ccel.org/ccel/schaff/creeds2.v.ii.i.html#v.ii.i-p36.4
  [2]: https://christianity.stackexchange.com/a/36114/1787