So how do they "find" these things? I live like 15 minutes away from Nintendo of America HQ down in Redmond. Can I just walk in and "find something?" I wonder... If I drove down there and dug around their dumpsters, what would I find??
Dumpsters are a thing, however that is often done as part of corporate espionage so be careful. Equally you will probably not find much other than boring office/factory stuff.
Some will actively contact people, others might be well known enough in a community for someone to reach out to (and not necessarily for engineering skills).
Otherwise when devs go bankrupt then not all bankruptcy agents will do things properly and things get out that way. This is where quite a few dev kits get found. Bonus is some bankruptcy places might just throw such things in the skip they bring in to clear the place.
Certain devs within companies or executives will get these things and neglect to return them to be destroyed if they fail.
Trade shows are nightmares to run so companies get brought in to handle them. Another potential source for things to get lost in the shuffle.
Other times they will be straight up stolen and avoid the shredder that way.
If it is built somewhere then you might have little ghost shift or beta/"broken" board thing get assembled or fixed up. Companies know this so programming might happen under stricter controls or things might happen in a few different factories.
With the internet then people sometimes realise what they have, especially when it is several years on and now people care -- nobody would really care if I had a custom colour 360 that microsoft decided not to release, I find a N64 with a never released but official custom shell and the kids would go nuts for some reason.
You occasionally get wives and kids selling off things at garage sales when people die but I certainly would not advocate going around looking for beta/unreleased stuff. If you are already buying games at such sales then go for it (I hear it is getting hard out there) but unless you have serious money to burn then I have not really got any good methods.
Short version if you do have some money or some time but not enough to go manual
Watch auction sites.
Watch local selling places (craigslist, facebook selling groups).
Figure out what sorts of forums normal people will find to ask about this sort of thing. I doubt many would come here,
http://assemblergames.com/l/ on the other hand...
If you have electronics recycling/dumps then let them know you will pay for such things (I have mainly only dealt in scrap metal and cars/industrial equipment around there, however the area is full of burned out hippies so there are several things handling types of electronics recycling). You will not be the only one though. Some of these things do not look pretty and if someone can't find a listing on ebay or something they will assume it is worthless tat and chuck it.
If you know house/estate clearance people then ask them. If you are collecting records, old books or furniture this is harder as others have figured this out before you but I do not know how many people tap them for games at the source. These sorts of people deal in bulk though so you will probably be buying a lot of crap (though stuff you could probably still sell) if you do head down this path.
Obviously you live in a good place for it but at the same time you face a variation on the silicon valley restaurant problem -- years ago it was noted that silicon valley was the place to be for tech, however as jobs were harder to come by then the people working in restaurants were likely as not to be new graduates with serious skills. Couple of devs sit down and think no pleb will understand what we are talking about, they were wrong and security/industrial espionage knew this and took advantage of it. If you lived in Minnesota then yeah you can probably get anything like that which comes up, not that it ever would really. Western Washington though is a different matter and there are probably self employed/work from home types with a "be there in 15 minutes" window and have a bunch of cash in hand.