They were already classified as an NFA firearm, that is everything in the NFA is a firearm first, then the actual designation being a subcategory.
I have not read the actual text of the law, but if all it does is remove the NFA category of suppressors, while leaving it considered a firearm which would require 4473 of course, then it seems to me it's legal status would be the same as the Mossberg shockwave and similar items. It is a firearm requiring the paperwork needed to sell a firearm, but it meets no other subcategory definition. Unless they make a new one for suppressors.
In that case it would be the same as any other firearm that wasn't NFA. State law notwithstanding, you can buy and sell privately without paperwork, building your own would be a possibility.
As for used suppressors flooding the market, I would think with the hurdles to suppressor ownership gone demand would far exceed supply for a while at least. I can see numerous new suppressor manufacturers as well as established companies diversifying into them. For Ruger after decades of being resistant to selling NFA items to the General public came out with a few suppressors that they sell now. I think other firearm companies would follow suit especially with no special NFA rules to follow.
In addition, since there is no added tax. The construction of them would not have to be durable enough to make them a lifetime purchase. Whereas now even the most basic 22 suppressor is a few hundred dollars at least, they don't need to be. A manufacturer could take a simple thin wall tube, stamp out simply designed baffles, and machine a couple end caps for just a few dollars. Being so cheap one will not have to worry about being able to clean it so simple assembly such as a groove in the end caps and the tube crimped onto it would make a very cheap assembly process. A simple suppressor for a 22 that might have a retail in the $30 range maybe even less. At that cost after firing a few thousand rounds through it and it may be getting less effective one would consider it disposable.
I remember seeing in one of the silencer books someone had a picture of suppresses being sold in a country where they were unregulated and indeed were encouraged to be used for noise pollution reduction. There was several in one of those little pop up display boxes like you see beside the register at a hardware store. Only instead of selling screwdrivers they were selling suppressors.
And no longer being NFA, quite possibly imported ones might become available.