The suppressor is not "married" to a specific firearm unless it is not removable from the firearm. Even with integrally suppressed guns that have the suppressors built onto the barrels, the suppressor itself gets the serial number, not the base firearm. That is the reason a lot of folks buy suppressors that thread on or quick-attach so that they can be used on multiple firearms. Some, like integrally suppressed barrels for a Ruger 10/22, can logically only be used on that model rifle/pistol; but the barrel can be used on ANY of that model without changing the classification of the base gun.
If you own a short-barreled rifle (SBR) and add a suppressor to the end, bringing the barrel length to >16", it is STILL a SBR and both the rifle and suppressor have unique serial numbers. But if you permanently attach a suppressor to a barrel, bringing the overall length to >16", that barrel can then be mounted on the rifle and no SBR is involved. Confusing? Welcome to the world of the NFA.