As debt-laden students head for degrees (that) they think will maximize their earning potential, many vital courses suffer. 

(that) they think will maximize their earning potential 这是嵌入式定语从句。定语从句本身是个主从复合句，they think是主句，that will maximize their earning potential为宾语从句，关系代词that并不在主句中作成分，而是在宾语从句中作主语。关系词所在的分句，嵌入到they think这个分句中作宾语，这种定语从句就叫做嵌入式定语从句 embedded relative clause。关系代词在定语从句中作主语通常是不可以省略的。但如果关系代词在嵌入式定语从句中作宾语从句的主语，则是可以省略的，而且是很常见的。

再给你一个嵌入式定语从句省略作主语的关系代词的例子：

This is the book my teacher says is very useful. book后省略了that。

网友可以在答疑网搜索'嵌入式定语从句“。