because和because of 都表示因为...
前者是个连词,后面接句子,如果是上面的句子就应该是：
She was sad because there isn't any chance left.
后者以介词of结尾,后面要么接名词,名词性短语或者句子,上面这个句子里面就是用的名词性的句子,把动词名词化,换成动名词.
She was sad because of there not being any chance left.
两句话都表示：因为没有任何机会留下了,所以她很伤心.