If you mail a book with DC and you can see that it has been delivered, but the person never marks it as such, does it go lost  in the mail??

Yes, it is declared "lost" by the system. The question of whether you get credit for the book depends on where you bought the DC. This is very well explained in the Help Docs: 

A book sent to an active member at PBS will not earn credit until the requestor marks it received, unless PBS Delivery Confirmation is used to send the book.  

• As the sender, you should call 800-ASK-USPS or go to http://postalinspectors.uspis.gov/forms/MLNtRcvd.aspx (the Postal Inspection Service's website) and input the information online there . This will help USPS try to recover your book if it truly has been lost in the mail.
• If USPS does return your book to you, and it is undamaged, you should ask the requestor (using the button on the Lost transaction in your Transaction Archive) if she still wants it.  If she does, you can re-send it.  If she does not, you can repost it.

If you sent the book with PBS-DC and it has been recorded as delivered by USPS:

• If the requestor has not marked the book received by a week after the delivery scan, contact us.  We will look into it.
• You will already have gotten your credit when the barcode was scanned by USPS. 

If you sent the book with DC purchased elsewhere and it has been recorded as delivered by USPS:

• Contact the requestor from the "lost" transaction in your Transaction Archive.
• If the requestor does not respond to your PM within a few days, contact us and we will look into it.
• We cannot grant credit for DC purchased outside PBS, but we can check if this requestor has become inactive.

If you sent the book with PBS-DC and it was never scanned (this does happen, rarely), contact us.   PBS could not give QuickCredit if our system was never notified of a barcode scan.  If your sending record is good, you will get your credit for sending the book.  This is the CreditAssurance part of PBS-DC.

Good question, Bertie.  I was in a similar position not too long ago, but since the receiver finally marked the book received, I was never able to find out first-hand whether the book would have been truly considered lost.

If you're ever in this position, I would suggest sending a polite PM to the receiver asking him/her whether they got the book and if they did, to please mark the book as received.

I did use PBS DC.  I did send her a pm . She should have gotten the book on the 1st of November. She didn't answer my pm.  So I was just wondering what would happen if she doesn't mark it received.

Try another pm just before the system declares the book lost (like 48 hours).  TPTB strongly encourage answering pm's in the case of possible problem transactions.  Therefore, if you again receive no reply you should refer the transaction to PBS Admin.  Since they do not look at all lost book transactions (DC or not), they will have no reason to look into this situation unless you let them know what's up.  If there's other items on the members account (missed dates or time-outs), it might be time for TPTB to take action.

If the requestor didn't respond to your PM in a week, Help Center says to contact TPTB

http://www.paperbackswap.com/help/help_item.php?id=319

If you sent the book with Delivery Confirmation and it has been recorded as delivered by USPS but hasn't been marked received yet:

• Remember that the book could have been scanned as "delivered" at the local PO, before it went to the requestor's mailbox--the actual delivery can be a few days later  Also, the book could have been misdelivered.
  • The requestor should check with her mail carrier about this package.
  • The package could also be at her local PO being held for pickup; sometimes pickup notices left by the mail carrier go astray.
• You should FIRST contact the requestor using the button on the transaction on the Books I've Mailed tab in My Account when a few days have passed after delivery.
  • If the requestor does not respond to your PM within a week, and/or has not marked the book received by a week after the delivery scan, contact us.  We will look into it.

I had a case recently where the wrapper arrived without the book.  I was supposed to let it go lost.  And it did and I got my credit back.  She got her credit due to DC.

However the rules state that if that happens the recipient is supposed to contact you.  It sounds from your post that has not happened.

If you use PBS DC, the site will also send an automated email asking the receiver to mark the book received.