I hear she quit her job.

Literal

She [topic-は] job [object-を] quit [hearsay-そうだ].

そうだ here is the hearsay marker (not the appearance marker), reporting information received from another source. The two そうだ are distinguishable by what they attach to: hearsay attaches to plain forms (辞めた + そうだ); appearance attaches to verb stems or i-adjective stems (辞めそうだ 'looks about to quit,' 寒そうだ 'looks cold'). 辞める ('quit, resign from') is the standard verb for leaving a job, with the kanji 辞 specifically reserved for resigning from work or office (compare with 止める, where 止 is used for stopping things in general).