He sent another fax informing Tom that the plan had been called off.语法问题

其实这个很容易解释
He sent another fax informing Tom that the plan had been called off
在当中加个逗号
He sent another fax，informing Tom that the plan had been called off
很明显的就可知道 做伴随状语 表伴随动作

非谓语动词，修饰fax
可换成定语从句，即 he set another fax which informed tom that the plan had been called off

表伴随
用来说明sent the fax的目的

作伴随状语..

做定于