。
She heard the story and was moved to tears.
Literal
She [topic-は] that story [object-を] hear [then-て] tears [object-を] shed.
涙を流す ('let tears flow') is the standard literary way to describe crying with emotion — more composed and dignified than 泣く ('to cry'), which can sound childlike or noisy. Linking the two clauses with て gives a clean cause-and-effect rhythm: hearing led to weeping. Stories or news that move someone to tears are a recurring trope in Japanese drama and ballads, where restraint amplifies the emotional payoff — the discipline of just letting tears fall, without sobbing, signals deeper feeling.