What happens when you ship a book and put DC on it. You know the person received it, but has not marked it as received.  Do they have a full month to mark it even though they did get it?

Because of possible USPS weirdness, you can't be a 100% certain that the person has actually received the book.  Or it's possible they are on vacation, lost computer access, or had other "life stuff" intrude. 

Yes, the DC scan has nothing to do with the time allotted by PBS to mark the book received. They have the full time, regardless of any scans.

Also, sometimes books are "Delivered" to the wrong address/wrong apartment. So, the scan may say delivered, but the person waiting for it still doesn't have it. Sometimes, they may never get it. So, the "delivered" scans aren't foolproof.

If it is close to the "going lost" date, and they still haven't marked it received, it is OK to send a PM just to ask if they did actually receive it. I've done that before and a few times people have told me they just "forgot" (for various reasons). I wait until 3 or 4 days before it is going to go lost to do this, however.

I always use PBS/DC so I have my credit.  Though I worry about people not receiving their book I've never PM'd to find out if they received it.  I've never had a notice that a book was lost.  I know I had one that was finally marked received on the last day before going lost.  That was the closest encounter I've had. 

I always PM to ask, just before it goes lost,  because I've had:

1. one person who had a bunch of books delivered on the same day from Amazon and "forgot" that this one came from PBS.
2. someone who was "busy with final exams" and forgot to mark recieved.
3. another person who "forgot" (no reason specified)

Per the Help Center, under "How do I use the PBS-Delivery Confirmation Tracking System?":

"USPS sometimes scans a package as "Delivered" when it reaches the requestor's local Post office

• there may be a few days' delay before the package reaches the destination address.
• If your package has been scanned as Delivered and has not been marked received a week later, please contact the requestor first using the PM button on the transaction.  If she or he does not respond to your PM within 3 or 4 days, please contact us, and we will look into it."

So, just cause the status is "delivered" doesn't mean the PBS member has the book just yet.

Cheers,
Catt