From the U.S. Treasury website (http://www.ustreas.gov/education/faq/markets/redemption.html):

"Bonds that are lost, stolen, mutilated or destroyed, can be replaced free of charge as long as it can be established by the Bureau of the Public Debt that the bonds are still outstanding. To assure that bonds can be traced, owners should keep records of bond serial numbers, issue dates, [etc.]"

I think we can do better than appeal to a fictional dramatization as authority.

Unregistered bearer bonds are definitely real. That's what we're talking about.

The difference between an unregistered bearer bond and other types of bonds is that the bearer bond is not registered to a particular individual, but instead guarantees payment for the bearer of the bond. Other bonds are registered with the social security number of the bond recipient.

However all bonds have serial numbers, regardless of whether they are registered. This is how the government verifies the validity of the outstanding debt guaranteed by the bond. Otherwise, what is to stop some counterfeiter from manufacturing fake bonds and claiming them?

I'm not sure what you're getting at. That bonds have serial numbers, much like dollar bills, has little relevance to the story at hand.