There are no firing guns, made for display only, they are regulated in no way.
There are Deactivated War Trophies which started as real guns but were basically welded solid so nothing can be made a real gun again.
There are Registered Dewats De activated war trophies that are registered with the BATFE as machineguns, but temp. are modified not to fire, they transfer as would any machinegun on paper except tax free, if/when someone reactivates a registered dewat then the $200 fee is paid at that time to make it live again.
A museum that gets federal funding can have in it's collection weapons that are illegal contriband. Often times when a war relic that was never legally registered turns up in an estate it will be donated to a museum which can keep it functional and save a bit of history from the cutting torch.
And a museum could own registered transferable pieces just like anyone can.