When the snows fall and the white winds blow, the lone wolf dies but the pack survives.
Because the faith of the Old Gods, the Stark’s gods, is strong like the Weirwood. It’s roots grow from dark places and dark memories: the Cave of the CoTF, Ned’s beheading, the burning of Winterfell. The Weirwood bends in the wood, but never breaks. You can try and destroy a Stark, but you can’t break them.