We've seen Littlefinger on the verge of death many times prior, and begging had never been his way. Aidan Gillen, who played Littlefinger spoke with The Los Angeles Times last summer and, when asked about the death scene, said, "I don’t think Baelish does crocodile tears. I don’t think Baelish likes to shed tears, certainly not in front of people." He added: "I don’t really think it was sentimental. I think it was involuntary: Your time is up."
From here, people might argue that a Faceless Man only wears faces of the dead, but we already saw that wasn't the case when Arya was forced to look into her own face at the House of Black and White in Braavos following her showdown with the waif and during her confrontation with Jaqen H’ghar.
With Littlefinger assumed dead, and the entirety of Westeros focused on the invasion from the north, Petyr Baelish would be left alone in the shadows to plot the next steps of his plan in solitude. The theory continues to say not only is he still alive, but that Baelish is actually going to be the hero of the entire story: "The prince that was promised."
The prophecy from the Lord of Light tells of Azor Ahai, a warrior that will wield a flaming sword and defeat the darkness. In this case, the darkness could be interpreted as the Night King and his forces, and the flaming sword would be a metaphor for the dragons, as opposed to the physical sword Lightbringer. And while Littlefinger doesn't really wield the dragons, they are present in Westeros because of wheels he put into motion. This part is more of a stretch.
At this point, we are only a couple of months away from getting answers to all of this, but it's certainly interesting to think about in the meantime. If Littlefinger is still alive, what is he up to? And could he be a legitimate contender to sit on the throne in the end?
Game of Thrones returns for its final season on April 14. The HBO drama stars Peter Dinklage as Tyrion Lannister, Nikolaj Coster-Waldau as Jaime Lannister, Lena Headey as Cersei Lannister, Emilia Clarke as Daenerys Targaryen, Sophie Turner as Sansa Stark, Maisie Williams as Arya Stark, Kit Harington as Jon Snow and possibly still Aidan Gillen as Petyr Baelish. The HBO series is an adaptation of the Song of Ice and Fire books by author George R. R. Martin.