Hearing my story, many students followed with their own stories of heads, arms, fingers stuck in places they shouldn't be.

they shouldn't be 是修饰 places 的定语从句。they  指前文的heads, arms, fingers。shouldn't be “不该在的地方”。

这个句子多少有点错误，错误在于关系词不能随意省略。

要么用where；

要么用 in which；

要么在 be 之后加介词 in，看作省略了关系代词 that/which。

1. Hearing my story, many students followed with their own stories of heads, arms, fingers stuck in places where they shouldn't be.

2. Hearing my story, many students followed with their own stories of heads, arms, fingers stuck in places in which they shouldn't be.

3. Hearing my story, many students followed with their own stories of heads, arms, fingers stuck in places they shouldn't be in.

【翻译】听了我的经历后，许多学生都跟着讲了他们自己的故事：脑袋、手臂、手指卡在了它们不该在的地方。

此外，该句还有一个错误，stuck in places where they shouldn't be，应改为 being stuck in places where they shouldn't be，把作定语的过去分词短语，改为动名词复合结构，作 of 的宾语。