At least in the US, private sales are legal, and there is no requirement to file any paperwork whatsoever.
Moreover, there is a staggering number of firearms that predate any sort of government record-keeping. It's not like these are muskets and black-powder revolvers, either - most of the designs for hunting rifles and shotguns are nearly unchanged from models that were available a century ago.
Moreover, there is a staggering number of firearms that predate any sort of government record-keeping. It's not like these are muskets and black-powder revolvers, either - most of the designs for hunting rifles and shotguns are nearly unchanged from models that were available a century ago.