afraid of waking her mother形容词引导的一个伴随状语吧.不知道你有没有学过非谓语动词,回想一下,分词做伴随状语省略引导词可以放在句中,比如说：The little girl,imagining herself being praised,started doing her homework carefully.
我觉得楼上说的不对,形容词引导的插入语应该和主句间不发生任何联系才对,很明显afraid of waking her mother的逻辑主语是the little girl