people suppose that he escaped disguised as a woman

哈哈．听我说
escape是不及物动词．后面什么都不用加就可以表达完整的意思－－－逃跑
disguised as a woman是一个独立的状态描述．是和逃跑伴随的－－－－－－伪装成女人．

这是个常见的伴随
i saw a fly in my soap, dead.
我看到汤里有只苍蝇．死了．

这里省略了by the way that he was
people suppose that he escaped (by the way that he was
)disguised as a woman.
人们猜测他用假扮成女人的方法逃走了。
也可以理解为伴随状语。

答案补充：
这句话这样说会更好理解：Disguised as a woman,he escaped.并不是escape+doing的结构。

people suppose that he escaped (by)disguised as a woman

省略了一个助词by
这样你好理解了么？呵呵

你是不是觉得它是由两个动词作谓语不正确啊？

如果这句话是对的话，我觉得disguised as a woman
是作为解释说明，he escaped 他逃跑，disguised as a woman 假装成女人，他假装成女人逃跑了！

人们猜测他是化装成妇人逃跑的。
语法没错。disguised as a woman是逃跑时的状态。

disguised as a woman 做状语成分,修饰谓语动词 escaped 表示逃脱时的状态是 伪装成一个女人