The evidence: Lord Petyr Baelish, aka “Littlefinger,” says his great-grandfather was originally from Braavos, aka the home of the Faceless Men and where Arya goes to be trained by Jaqen H’ghar to be the assassin she now is, aka “no one.” Perhaps Littlefinger is a descendant of the Faceless Men himself, or perhaps he has enough connections with the Faceless Men to pay one off to take his place and “die” at Winterfell at the hands of the Stark siblings, while the real Littlefinger is off in hiding?
He’s also the slimiest character of them all. He brought about the War of the Five Kings by convincing Lysa to kill her husband, Jon Arryn, then hand of the king to Robert Baratheon. He also betrayed Ned Stark (which caused him to be beheaded), attempted to kill Bran Stark, killed Catelyn Stark’s sister, Lysa, and…yeah, he’s basically responsible for everything bad that’s happened on the show since day one.
But through all of those crimes, he’s magically managed to stay alive and not get caught (until Bran used his three-eyed raven skills to time travel and confirm all of Littlefinger’s horrifying deeds). So, could he get away with faking his own death too? Seems likely.
Season seven, episode five also sheds light on the “Littlefinger as a Faceless Man” theory. In one scene, highlighted in this YouTube video by Neo, a woman whispers “your time is up” to Littlefinger during a secret meeting at Winterfell, then hands him what appears to be a coin…the coin of Braavos, perhaps? If she traded places with Littlefinger, the real Lord Baelish is still alive and well, while this mysterious woman is the one whose throat was actually slit by Arya.