I'm assuming this is in reference to the so-called
"Prophecy of St. Malachy", a prophecy allegedly by the 12th-century St. Malachy regarding the next 112 popes. For each pope, a short and brief description of 2-4 words is given, and for the last one, "Peter the Roman" (Petrus Romanus) it tells us:
"Peter the Roman, who will pasture his sheep in many tribulations, and when these things are finished, the city of seven hills will be destroyed, and the dreadful judge will judge his people. The End."
If the prophecy is right, then we won't be seeing Peter the Roman after Francis, because Francis
is "Peter the Roman" by the count. Indeed, should Francis die without the above things happening, it would seem to demonstrate the prophecy was wrong.
But there was little reason to put any credence into this prophecy anyway. Although Malachy lived in the 12th century, this prophecy was first "discovered" in the in the late 16th century. That doesn't by itself make it false--various documents get lost and then found later--but the problem is that while all of the descriptions of the popes for
prior to its discovery fit perfectly, immediately afterwards the attempts to link them up to the actual popes become significantly more forced. This is exactly what one would expect if this was manufactured: It's easy to "predict" things when referring to the past, but not so easy to predict things in the future. It is believed that it was concocted in order to grant credence to Girolamo Simoncelli in the next papal conclave (as the prediction for the next pope was "From the old city" which fits him perfectly, but you have to stretch things to fit the actual next pope).