I am totally uncertain about what would be done with a post 1968 firearm with an altered serial number in the US. In fact even in Canada I would have to make a phone call to find out, obviously if I were buying such an item I would simply steer clear of the whole thing. However sometimes folks do turn up firearms during home renovations or other legitimate circumstances, and in some cases have been allowed to keep them after completing the correct process.
When we had our Long Gun registry, and the "problem" of un-serialized firearms came up, there were a number of interesting solutions. Some people would assign their own serial number, based on whatever they chose, some were applied with stamps, others with electropencil and dremal tools, others where crudely scratched into the metal with a sharp instrument. The official means would be to apply for a serial which would be issued by mail on a tiny gold foil sticker, which was then applied to the firearm by the owner. As a footnote the stickers were not durable under normal handling. The group in charge of the registration either did not care, or was not knowledgeable enough to ask how a Cooey Model 60 (example of unserialized production firearm) came to have a serial number at all. (Just minor historical observations/commentary)
The serial numbers either officially or unofficially assigned to firearms had no real life application to the make, history, production date, or brand of the firearm, which I am sure may puzzle future collectors trying to establish provenance of any of these guns. Luckily most collectible military guns were heavily serialized so they were mostly spared from the "Bubba Compliance" scratchings and stampings.