All the claims that the next Pope will be the last one are based on non-biblical "prophecies" of an Irish priest named Saint Malachy (1094-1198). He supposedly prophesied that there would be a total of 112 popes, beginning with Pope Celestine II who served one year from 1143 to 1144.
Actually no one knows for certain where the prophecies came from. Wikipedia states, "The prophecy was first published in 1595 by Arnold de Wyon, a Benedictine historian, as part of his book Lignum Vitæ. Wyon attributed the list to Saint Malachy, the 12th century bishop of Armagh in Ireland. According to the traditional account, in 1139, Malachy was summoned to Rome by Pope Innocent II. While in Rome, Malachy purportedly experienced a vision of future popes, which he recorded as a sequence of cryptic phrases. This manuscript was then deposited in the Roman Archive, and thereafter forgotten about until its rediscovery in 1590. On the other hand, Bernard of Clairvaux's biography of Malachy makes no mention of the prophecy, nor is it mentioned in any record prior to its 1595 publication. Some sources, including the most recent editions of the Catholic Encyclopedia, suggest that the prophecy is a late 16th century forgery."
Like the so-called prophecies of Nostradamus, the prophecies of Malachy are very obtuse, and can be interpreted only after the fact. In each case some object or location is mentioned that is tied to the pope being prophesied. For example, Alexander III who served from 1159 to 1181 is referred to in the prophecies as "out of the guardian goose." The fulfillment of the prophecy is said to have been in the fact that his family's coat of arms had a goose on it. Celestine III who served from 1191 to 1198 filled the slot designated for one "from the cattle country." He was supposed to have fulfilled that prophecy because he was from the Bobone family, and those who believe in the prophecies claim that the family name is a wordplay on cattle (boves). Bringing the prophecies up to date, consider what was said of the slot that John Paul II filled (1978 to 2005). He is described as "from the labor of the sun." His fulfillment of that prophecy is supposed to rest in the fact that he was born and entombed on the day of a solar eclipse.
Another problem with the prophecies is that it is not at all clear that Pope Benedict XVI is really the 111th, or next to the last pope, in the series. That's because there were a number of conflicting popes or anti-popes during the time from 1143 when the numbering began.Approach Malachy's prophecies warily, for they're extra-biblical. We can always be sure of prophetic fulfillment when we stay to the biblical text alone.