TL;DR version: When Shireen was sacrificed by Stannis in HBO’s “Game of Thrones,” a semi-popular theory that Jon Snow will be risen from the dead through a sacrifice of Shireen took a hit.
“A king’s blood. Only a king’s blood can wake the stone dragon.”
-ASOS, Davos IV. Spoken by Melisandre.
It’s not canonical — because it’s the TV version — but a semi-popular theory that contends Jon Snow will be risen from the dead by Melisandre via a sacrifice of Shireen took a hit when Shireen was sacrificed for different reasons on the snow.
The theory is contingent on R+L=J being true; that is, that Jon Snow is a Targaryen, and therefore a dragon.
Shireen is the “king’s blood” that would be used to wake the “dragon” (i.e. Jon). The “stone” part of the quote can be applied to both Shireen (through Greyscale, the disease that made face stone-like) and to Jon (him being presumably dead in the wintry north would make him stone-like.)
Why the Shireen sacrifice theory took a hit
Because she was sacrificed to keep the snow away on the show, not to bring a different kind of snow — Jon Snow — back from beyond.
Did the show spoil the books here? We’ll have to wait and see. Book Stannis has more of a spine when it comes to saying “no” to Melisandre than Show Stannis, but we’ve entered uncharted territory here.
Proponents of the theory will point out that Shireen is still alive and at the Wall in the books, which is where she needs to be if the Shireen sacrifice theory is to come to fruition.
Others might point out that if Shireen is to be used to resurrect Jon Snow from the dead in the books, that would be a major, major change for the show to make.
In short, The Shireen sacrifice theory is still possible, but it’s not as strong as it once was.