If Stannis dies, Davos rallies the army to the only person in the North who can be trusted as a leader: Jon Snow. That puts Jon in charge of Stannis's armies, the wildlings and the Night's Watch, which will help him fight the Walkers, but he then sends a message to everyone to send help, which of course is picked up by Daenerys.
In the meantime, the South probably descends into chaos because of Tommen's misrule, so when Dany and Jon stop the Walkers, the only thing left is for them to just walk south together.
ἡ δὲ κἀκ τριῶν τρυπημάτων ἐργαζομένη ἐνεκάλει τῇ φύσει, δυσφορουμένη, ὅτι δὴ μὴ καὶ τοὺς τιτθοὺς αὐτῇ εὐρύτερον ἢ νῦν εἰσι τρυπώη, ὅπως καὶ ἄλλην ἐνταῦθα μίξιν ἐπιτεχνᾶσθαι δυνατὴ εἴη. – Procopius
Ummaka qinnassa nīk!
*MySmiley*