可以这样改.that还可以换成which.即：
The documents that/which they were searching for have been recovered.
但是,原句“The documentsfor which they were searching have been recovered”中的which就不能换成that了,因为它紧跟在介词for的后面.
如果把for which they were searching这个定语从句还原成独立的句子,就是：
They were searching for the documents.
search for 寻找