Matthew 16:18

> And so I say to you, you are Peter, and upon this rock, I will build my
> church,* and the gates of the netherworld shall not prevail against
> it.

Is there any teaching of the Catholic Church on when it can be considered the end of its existence by definition?
Clearly, it is not the death of the pope as the new one can be elected. Is there a time period how quickly the pope needs to be elected and if not met the institution ends? I doubt there is.

Would that be if the last person who was baptized in the Catholic Church die? Can we then say this is the end of the Catholic Church on Earth?
We still have the communion of the saints so basically, it will never cease but I'm asking on Earth.