Arcanum: Steamworks and Magic Obscura. Play a tech character. It's an RPG, but it's a pretty decent one, and it does feature the scavenging + crafting that you wanted. But you won't feel like you're playing a straight scavenging game like you wanted. It has a strong linear plot.
Here's a reason why it might not have been explored very far: So you've scavenged this loot; now what do you do with it? You've been picking up the leavings of other peoples' fights, so what are you fighting on your own? And what happens when you run into the people who left that scrap in the first place? Does the game just stay low-powered for the whole game, or do you fight people who don't leave any loot at all?
It's a staple of any games with inventory that when you kill someone, you take their stuff, and raise your power level to theirs if you were weaker. Hell, even Doom let you take shotguns and chainguns off the zombies who were using them, and they also gave you tons of ammo. On the other hand, when Doom set you against imps and stuff that didn't drop weapons, the game changed a lot. So I guess the combat would be fighting against people who did NOT use scavengable components, and maybe the people you're scavenging from are long, long dead, technology having been reduced considerably.
This is the sort of setting that would work great in, like, an anime or something; something where a rare and extremely valuable find would be a plot device instead of a balance-breaker.
You could fight animals that don't use tools. Some animals would have useful parts like hides or edibles. Other animals would be like jellyfish or blobs or gasbags, or otherwise non-useful like worm creatures. In any case animals don't drop loot but they can be tough.
There's also robots you could fight. When you beat up a robot it will ruin a lot of components. If you electrocute it, the physical parts will still be good but not the electrical parts. Maybe you could find a weapon that would just destroy physical parts but leave some electrical components? In any case, this would net you more scrap rather than useful loot.
Another scavenger will probably only be a challenge if he has a better weapon than you. So you're probably fighting single scavengers at low levels, more scavengers at a time at high levels. This means you don't have a 1:1 fight where the scavenger enemy needs to have better and better equipment. Once you have melee weapons, you don't need or benefit from more of them, so scavengers can easily have those. They can also have thrown weapons like sharp rocks, wrenches, skillets, knives, and spears. A scavenger could carry a molotov cocktail or a grenade, and if you incapacitate him before he can use it you'll get a piece of good loot. But it's still a one-shot thing, and he could throw it before you kill him.
He could also have substandard missile weapons like a weak bow or sling. These cannot really be broken down for spare parts. If he had a crossbow you might be able to break it down and use the parts in your own crossbow, or for some other invention. So bows and slings should be common missile weapons.
Another scavenger with a legitimate weapon like a gun might still not represent much of an improvement. The scavenger will start the fight with some ammo, but not a ton. His gun will probably not be pristine. If you seize his gun and it's the first one you found, you'll have several shots of ammo and the gun will probably last for several dozen or even a hundred shots before you need to repair it. Furthermore, perhaps his ammo is completely different from yours. Fallout 1 and 2 had a great way of making you choose which guns you wanted to use. If your game has 20 ammo types, and ammo / guns spawned used them all evenly, then the player has to make some choices.
He can leave behind a lot of ammo. Or he can take it and sell it, losing much of its value. Or he can accept the opportunity cost of carrying multiple weapons or the time cost of traveling back to his stash (which could be raided in his absence) to change guns when his current ammo runs out.
A higher-damage gun might require special ammo that contains a rare component. This makes using the gun an interesting choice, because it's like a boss fight sort of thing. If you don't know when boss fights are coming in advance, though, then leaving the powerful gun at home will mean you never use it.
Your own equipment degradation should be minor. That is, it degrades reasonably fast but when it hits bottom the gun still works, just poorly. Maybe it jams more often or the accuracy goes down. This encourages you to repair without making it an absolute requirement. It's possible to play a marksman who is not a repairman. The same should work for armor: it degrades rapidly but when it hits bottom it's at much-reduced effectiveness but it still does work.
This means much of your scavenged stuff will go toward repairing your own gear rather than making new gear.
The next step, after you have a pretty good set of gear and you're starting to collect surplus junk, would be to build a vehicle or fortify an area of the scrapheap.
The vehicle will require fuel, which means you probably want to make a Fuel Distiller. You need to put organics and certain scavenged minerals into the Distiller, so there goes some of your loot. The Distiller itself is a magnet for scavengers and it gives off a sweet scent that attracts predatory animals. This means you probably want the Distiller in a fortified area, or else hidden well away from your own home. Either way it becomes an oasis both for you and for everyone else.
Fortifying a section of the scrapland will require much scrap and labor. But this blocks off a space that you can use for your own purposes.
As you encounter other scavengers, if you have a reputation for trying to talk, they might approach peacefully and ask to trade. If they see you are well-off, they may leave and give information about your activities to raiders. But they might instead come back later and ask to join you. You can of course refuse.
Having scavengers under you means you need to protect them and support them. But they will go out and scavenge and bring back a tithe to you, sort of a tax. You can demand more tax, which can have undesirable effects. If you are very lenient, they may not work as hard, but if you're very strict they may flee. You can also ask them for certain scrap so you can make things for them; for example, you ask Joilie the Sniffer for six Sheet Metal because you want to make her some Snazzy Metal Armor. She agrees to the hypothetical trade, giving you the sheet metal in exchange for nothing. She expects that you will give her the Snazzy Metal Armor for nothing, and if you don't she may be upset. You can also ask them individually or set up a bulletin board to tell them what you want them to collect. In this way you can equip your followers as you like.
Eventually a large settlement will attract raiders even if everyone is loyal and not a spy. There will probably be emergent behaviors like attempts at a truce (honest or false), sneak attacks, attempts at bribing your people, and maybe kamikaze attacks. You will probably have to sally out into the raiders' camp to break and scatter them so they leave you alone. You can bring some scavengers with you in the attack!
Doing this will raise the threat rating of your little settlement. If your threat is high but your wealth is low, nobody is going to attack you. It should be easy to keep threat up above wealth unless you really focus on luxury and refuse to build your strength.
But the size of the settlement doesn't really get above a few dozen. Scavengers don't like to form permanent groups, and the scrap heap around the settlement will soon be gleaned. They will need to roam outward, and going farther from home on expeditions will cull the herd. A large settlement also encourages free riders (laziness), crime, and infighting. At some point malcontents may form a splinter group, which you must drive off or kill lest they take over the settlement. Population growth from immigration will slow greatly as most scavengers have some amount of Loner stat and will shy away from large groups. You may even see some of your current scavenger-citizens leave because they don't like how big the place has become.
And you could always just leave if you got tired of it.