I've had this happen to me as well. PO showed delivered, but I never got it. Post Office won't do much except ask the delivery person. I had to file a local police report and a report with the Post Office police on-line.
As far as your responsibility goes, you're not going to like it if your buyer paid by PayPal. Insurance is for the seller not the buyer. Never, ever send something uninsured unless you can afford to take the hit if it comes up missing. PayPal has specific rules about what how items are sent. If the bag was more than $250 PayPal requires signature upon delivery not just DC. PayPal will find in her favor if this is the case here.
She could also try a charge back with her credit card if that's how she paid. She would probably need to file a lost or stolen package report on-line with the postal police, but she may well be successful at that as well.
When this happened to me I didn't want to make a PayPal claim or do a charge back because I was familiar with the seller and didn't want her to get hurt just because she didn't have signature confirmation. I checked with my credit card and found they offered insurance on lost or stolen packages. I made an insurance claim and got my money back. As I said, I had to jump through some hoops and file a couple of reports, but it was basically painless. You could ask if your buyer might have this option. It's not fair for the seller to take the hit when the post office messes up.