BEIRUT, Lebanon — President Bashar al-Assad of Syria sits in his mountaintop palace as the tide of war licks at the cliffs below.

Explosions bloom over the Damascus suburbs. His country is plunging deeper into chaos. The United Nations’ top envoy for the Syrian crisis, Lakhdar Brahimi, met with Mr. Assad in the palace on Monday in an urgent effort to resolve the nearly two-year-old conflict.

How Mr. Assad might respond to Mr. Brahimi’s entreaty depends on his psychology, shaped by a strong sense of mission inherited from his iron-fisted father and predecessor, Hafez al-Assad; his closest advisers, whom supporters describe as a hard-line politburo of his father’s gray-haired security men; and Mr. Assad’s assessment, known only to himself, about what awaits him if he stays — victory, or death at the hands of his people.

From his hilltop, Mr. Assad can gaze toward several possible futures.

East of the palace lies the airport and a possible dash to exile, a route that some say Mr. Assad’s mother and wife may have already taken. But the way is blocked, not just by bands of rebels, but by a belief that supporters say Mr. Assad shares with his advisers that fleeing would betray both his country and his father’s legacy.