This is the first time this has ever happened to me. I  received an envelope from the post office with an empty wrapper inside it.  The book is due to go lost sometime next week, I think. So what do I do? Do I just wait for it to go lost? Do I PM the person who sent me the book to let her know what happened?

Don't mark it received, you didn't receive it. PM the sender and let them know.  The sender than can contact USPS as outlined in the help center-

• The sender should call 800-ASK-USPS or go to http://postalinspectors.uspis.gov/forms/MLNtRcvd.aspx  and input the information online there. This will help USPS try to recover the book.

  • The form is titled "mail Theft"; this does not mean that you can use it only if you think the book was stolen.  "Received without contents" is an option on the page.
  • The choice to make under "Class" on the form if Media Mail was used is "Parcel Post".

It's very unsettling when this happens - isn't it?  I got an open box with all sorts of weird fabric and who knows what to call it(?) along with a label with my name on it!  I didn't recognize it as a PBS label - but I didn't recognize any of the stuff they delivered with an "apology" for it being opened (destroyed).  It was very weird.  My DH and I shook our heads over the entire thing for days!

Ruth