A serial number does not allow a firearm to be traced beyond the initial sale.
If a firearm is recovered at a crime scene, and the powers that be want to know who owned it, they call the manufacturer.
The manufacturer gives the name of the wholesaler it was sold to. When the wholesaler is contacted, the name of the retail establishment is given. When the retail establishment is contacted, the name of the original purchaser is given. There is no requirement for the retail establishment to keep the data beyond 20 years.
The BATFE then attempts to contact the original purchaser. If this person is unable to account for the disposal of the firearm, the trace ends here. There are a bazillion reasons the original owner may not be able to account for the firearm. They include death, dementia, theft, loss, private sale etc..
When I purchase a used firearm, I give the seller a receipt that includes an accurate discription of the item purchased and the sellers identifying information. Should the BATFE ever show up on their doorstep, they are able to refer the investigator to me. My records will show my disposition of the firearm. This is the only was a trace by serial number can go beyond the original purchaser.