Here is what I have found. I was and FFL dealer in the early 80's.
Unregistered Weapons
The trick is to have an unregistered weapon, and specifically for this post, an unregistered weapon that you legally built yourself.
On an AR-15, the serialized portion of the firearm is the lower receiver. That is the only part that requires an FFL transfer (background check, etc) to purchase. Everything else can be purchased without an FFL, but without the lower receiver, these parts are just paperweights.
So in order to have an unregistered AR-15, you must have a lower receiver that does not have a serial number, and therefore does not require an FFL. The easiest way to do this is to get an unfinished lower receiver, also called an 80% lower receiver (I’ve also seen 95% lower receivers), and finish the receiver yourself.
What is an 80% Lower Receiver?
An 80% lower receiver is a partially completed piece of material that requires special tooling and skills to be completed and considered a firearm.
Legality
How can this possibly be legal?
I'll try to find the paragraph in the law when I can.
Take a look at what is required to finish the lower. One item is a Drill Press... the holes need to by drilled.
It takes some work, but (and this is without legal reference) what it gets you is a weapon that is not registered and is not required by law to be registered. Again, this is without a current legal reference.