The only way to know “for sure” is to see what got put on that 4473.
Most FFLs “know better” and if they see an AR lower they’re going to check the box for “OTHER” so you can assemble it however you want.
Keep in mind, as posted above that however you build it FIRST is what will classify it. So if you build it FIRST as a rifle, then it will forever be a rifle. If you build it FIRST as a pistol, then it can be a pistol or a rifle later. I’ve seen some folks will assemble it as a pistol, take a picture of it and label it as “the first build” as proof of the FIRST build… and then they can go back n forth and will always have that pic as proof that it was originally a pistol.
If you’re FFL went out of business… Yikes. If they sold to someone else, then that someone else has the paperwork. But if they totally folded… then they are required by law to give that paperwork to the ATF
In general the rule for FFL’s is that they must retain the 4473 for SEVEN years then they can be destroyed as it literally becomes a fire hazard and storage nightmare.
BUUUTTTTTT
the bound register (log book where every page is numbered) is required to be maintained as long as the FFL is active. If a new store owner shows up he has to get his own FFL and start a new bound log (now computer legal). The retiring FFL MUST turn in the bound ledgers to the ATF at the close of the FFL. If it’s a LLC or INC that changes hands, the new “owner” must maintain the previous logs.
It has been too long for me to remember what was recorded in the bound log to be accurate. God help you if your computer crashed with a electronic “bound log” and you didn’t have “per purchase” backups.
If they ran the S# as you say, it would say YOU were the last purchaser not anything else. That is a time consuming effort as usually “THEY” are in possession of the stick and start with the MFG, then the Distributor, then the Dealer, then your dealer and finally they knock on your door to find out who YOU sold it to. FWIW they REALLY don’t like the “Some dude in as suit offered me $1000 for it so I sold it to him.” the only one they hate more is “I lost it in a poker game.” Or so I’ve been told