You might ask yourself: who is this girl in the room and what became of that friend of hers?

became 是动词 become 的过去式，表示"变成、成为"的状态变化。 of 是介词，在这里表示"关于...的情况"或"...的"关系。 became of 是一个固定搭配，表示"某人/某物后来发生了什么变化或处于什么状态"，常用来询问人或事物的最终去向或结果。