What This Means For Game Of Thrones Season 8
If this theory pans out, it means that season 8 could play out very differently - because Littlefinger hasn't bled out on the floor of the Winterfell hall, but is still alive, still scheming, and somewhere else entirely. It's possible that he has headed back to the Vale (leaving the soldiers at Winterfell behind), where he is still Lord Protector. With the news that it looks like Robin Arryn is going to be in the premiere episode, Petyr could definitely be returning to the Vale and his 'step-son' to set up for his next move.
As for his plan, it seems unlikely that Baelish would return to the Lannisters, as they know that he isn't to be trusted, but it is possible that he could attempt this. It's also possible that he would attempt to take down the Stark family, but given his obsession with Catelyn, it seems that he may not take self-preservation that far. However, having been revealed to be a traitor by the Starks, this also means that he would be unable to go to Daenerys and throw in his lot with her as future Queen.
However, he may well have a much bigger plan, and one that doesn't end up with him as Hand, Advisor, or scheming brothel-owner. Littlefinger may well go for the throne himself. He would be able to use the chaos of the White Walkers and the tug of war between the Lannisters and Starks to make his way to the absolute top. This may have even been a long game he's been playing the whole time, as it has been revealed that he orchestrated a lot of the Lannister/Stark conflict in the first place. He may not have a claim to the throne, but he's clearly a fan of rising despite family name, and has all the information that he needs to manipulate anyone into accepting him in a time of chaos. And with the Starks and Lannisters under the impression that he is dead, Littlefinger would be able to scheme his way to the throne unopposed.
Could This Just Be A Result of Game Of Thrones' Ending Struggles?
Of course, this theory is very much in the realm of speculation, and it's possible that there is a much simpler explanation for Littlefinger's out of character death and conversation with a young woman in Winterfell. It could be that the young woman was a spy, or otherwise simply working for Littlefinger, and that he died because he simply became over-confident in his ability to manipulate Sansa and keep her for himself.
This is a strong possibility, especially when considering the timeline of the series. At this point, the final season looks to be focusing almost entirely on two conflicts; the Stark/Lannister battle, and the battle between the living and the dead. There are multiple loose ends to be tied up along the way, including the fate of Gendry as a potential heir to the throne, and with only six episodes to do it all in, it seems unlikely that the writers would want the added complication of a secretly-alive-Littlefinger in there as well. It's very likely that Littlefinger was finally killed, not because he faked his own death, but because the writers needed to kill him off before the final season.
Either is possible, and if Littlefinger is back, that will definitely make for some interesting final-season politics (and an absolutely furious Sansa, which would be amazing to see). However, if he is actually dead, at least fans have the satisfaction of knowing that he really did get what was coming to him.