I have swapped many books here and this is the first time this has happened to me. 

A person requested a book from me over the weekend.  I accepted it and wrapped it and it is ready to go to the post office this afternoon.  I just got an email from the requestor saying that she just received my book and can't mark it "received" since I never marked it "mailed".  Well I haven't mailed it yet.  So, what I think happened is that her first request for this book timed out and the request then went to me.  The first person mailed it but never mareked it mailed as she has it in her hands.

Now what?  If she cancels this request from me will my book go back to then end of the line or will it be the next in line when someone requests is?  It is a book with lots of copies available but is moving fairly quickly.  If it is next in line I think I will get another request for it in March sometime so no biggie for me.

What should I tell this person to do?

If she cancels, you would keep your place in line. The problem is that since you already printed the label she can no longer cancel, you have to, which would remove the book from your bookshelf. What I would do is send in Feedback via the Contact Us link in the lower right Company. Let the Team know in the Feedback what happened and ask that they cancel the transaction in a way that will return your book to its previous place in the FIFO line since the receiver got the book from the previous sender.

Then, once your transaction has been taken care of by the Team, PM the receiver and let her know that she can mark that copy as received by going into her Transaction Archive and finding that book with that sender's name on it and clicking on the [Was This Book Received?] button.

What Melanie said 

Thank you, I let the team know what has happened and are waiting to hear back from them.