they were surprised to hear of his death.
to부정사의 부사적용법- 감정의 원인!!!으로 쓰였다고 알고 있는데요

they were surprised hearing of his death.(x)라고 교재에 나와있더라고요

하지만 제 생각에 they were surprised [[분사구문의 시작]]hearing of his death.

이렇게 보면

they were surprised because they heard of his death.가 분사구문으로 축약되었다고 볼 수 있어서 두번째 문장도 맞지 않나요?^^;