Not every Megarian made puzzles the center of the school's work. Stilpo, who led the school in the late fourth and early third centuries BCE, turned it instead toward an ethical teaching close in spirit to Cynicism, arguing that the wise person achieves apatheia, freedom from disturbance, by recognizing that nothing external, wealth, reputation, even a besieged city, is truly one's own to lose. When Demetrius Poliorcetes sacked Megara and offered to spare Stilpo's property, Stilpo is reported to have answered that he had lost nothing, since he carried everything that was really his, his learning and his virtue, within himself, an anecdote later writers repeated as the cleanest statement of the position.
The teaching mattered less for what it said than for who heard it. Among Stilpo's students in Athens was a young Cypriot merchant named Zeno of Citium, who studied with him before founding his own school in the Painted Stoa, and Stoic ethics preserves recognizably Megarian fingerprints in its account of what is and is not within a person's control and in its own use of apatheia as a term of art. The logical puzzles for which the Megarians are chiefly remembered and Stilpo's ethical teaching for a time ran through the same school, and it is the ethical strand, transmitted through Zeno, that reached the widest later audience, carried forward inside Stoicism long after the Megarian school itself had no members left to defend the liar paradox.