The narrative arc of the series appears to be the rise, fall and rise again of House Stark. The original title for Book 7 was A TIME FOR WOLVES until GRRM felt it was a bit too spoilery, so I think that indicates that the Starks will return to power at the end of the series.
How that is accomplished - through Bran's warging, Possibly Undead Jon Snow perhaps getting Robb's letter of legitimisation (and if it matters by that point), Rickon inheriting Winterfell or possibly Sansa's machinations in the Vale - is unclear, but there's quite a few Starks left (in real terms we've only lost Ned and Robb; Catelyn wasn't really a Stark but is still alive - or undead - anyway) to pick up the slack.