No, she didn't die & there was a rumor about that but John Green wrote on his tumblr that wasn't true.
link
"There is a post going around tumblr with tens of thousands of notes saying that I “announced” that a certain character in my book The Fault in Our Stars dies one year after the end of the book.
1. I have never said, written, or thought any such thing. (Photoshop is magic!)
2. If I had said, written, or thought any such thing (which, again, I did not), it would not become true. As you’ve probably heard me say a gajillion times, I don’t think the voice of the author should be privileged when it comes to matters outside a book’s text. So if I ever make such an “announcement,” I don’t think it should carry more weight than any other reader’s speculation.
I ended The Fault in Our Stars where I wanted to end it. I have never said anything about what might happen before or after what’s depicted in the book. I finished writing it, for better or for worse, and it now belongs to you."
-John Green -