A judge sentencing someone to death doesn't mean they immediately drag the person out and shoot them. There is a very long process involved, where the execution is generally delayed for 2 years, unless the crime committed is particularly severe and warrants immediate execution.
Drunk driving that results in hitting someone, without the perpetrator actively fleeing the scene, clearly doesn't qualify for immediate execution.
Thus, the guy who killed He Qingyan and her two daughters is, for the time being, still alive.
"Judge Sun is truly a good judge, sparing his life like that. If it had been up to me, I would have killed him long ago; he wouldn't still be alive," said Huang Yuntao.
Seeing Huang Yuntao's competence in investigating Xu Jiawei and Kang Yurong, Shen Siyuan realizes he has connections and wants his help in investigating the person who killed He Qingyan and her daughters.