句子没有错误。long for：渴望某人或某物。unburden oneself to somebody: 向某人倾诉自己的苦衷或烦恼。whom引导定语从句，并在从句中作介词to的宾语。非正式语体可以用who，that引导从句，也可以省略关系词。本句用whom为正式语体用法，但介词to留在最后又是非正式用法，所以显得有些别扭。可以作如下改动：
She longed for a sympathetic person to whom she could unburden herself. 正式语体
She longed for a sympathetic person who she could unburden herself to. 非正式语体
She longed for a sympathetic person that she could unburden herself to. 非正式语体
She longed for a sympathetic person she could unburden herself to. 非正式语体
但原句并没有语法错误。句子意思为：她渴望有一个能对其倾诉苦衷的善解人意的人。
