Whatever作为疑问代词，跟what的用法一样，what+ever只是为了强调，即：强调询问的语气。意为“究竟，到底”：You use whatever to ask in an emphatic way about something which you are very surprised about.  

Whatever can you mean?你到底是什么意思？

Whatever is the matter with you both?你们俩究竟怎么回事？

你的句子Whatever are they afraid of? 中的whatever就是上述用法。不引导从句，只是作介词of的宾语。