In the Two-Dimensional World, your surroundings are always enveloped in lines, the only distinguishing factor being the brightness.
The darker the brightness, the further away these lines are from you.
The current situation indicates that there are neither two-dimensional creatures nor buildings nearby, just vast open land; these are the characteristics of the outskirts.
Yu Liang, having escaped from the school, did not flee north following the north gravity, but instead, he chose to flee south.
The Flat Kingdom now believes that all the player paper-figures come from the extreme north, so they definitely strengthen the northern border defenses, strictly limiting entry and exit. Fleeing north would be like walking into a trap.
And what use is escaping from the Flat Kingdom anyway?
They are not spies sent from the extreme north. For the sake of peaceful relations between the two countries, why would the extreme north protect these paper-figures whose origins they don't know?