captured doing espionage or propaganda，整体是过去分词短语，作 over 200 of them（两百多名间谍）的定语，而且是非限制性定语。

在这个过去分词短语中，又包含着一个现在分词短语 doing espionage or propaganda，它作了captured 的时间状语。说明是“在进行间谍活动或宣传时（被捉）”。

原句相当于：

In the filthy jail in Sianfu there were over 200 of them, who had been captured while/when/in doing espionage or propaganda.