The only time I have heard that a serial number could be applied to a firearm was where the firearm was stolen, recovered with the serial number removed, and the BATF authorized the serial number to be replaced. Otherwise, you are back to someone stealing a firearm, removing the serial number, and getting the BATF to authorize a new serial number.
It is illegal to possess the firearm with a removed or altered serial number, so unless the firearm was yours and originally listed on a theft report, how do you explain the missing serial number? As someone mentioned, it just isn't worth the risk of losing you right to own a firearm to keep something of low value and high risk.
http://www.ecfr.gov/cgi-bin/text-idx...3.1.17&idno=27