What do you mean "source for a single CPU socket"?
What are you ACTUALLY looking for? A CPU? A motherboard? The socket itself, as a replacement part?
If you are looking for a replacement socket, then my advice would be to just forget that. The cost versus the price of simply replacing the board, isn't justifiable for anybody who doesn't have the experience and tooling to do this job, and if you had that, you wouldn't be here asking this question. That is no slight to you, and doesn't indicate that you are not intelligent enough to do the replacement, but even professional repair technicians generally would replace the board, not the socket, because it is time and labor intensive, difficult, and hard to justify when a replacement board is much cheaper.
Plus, the success rate of replacing a board over replacing the socket, is much higher. Yes, there ARE sources out there for replacement sockets, to some degree, but it just doesn't make sense in 99.9999% of situations.
You'd be surprised what SOME seriously intent individuals can accomplish with the right setup and tooling. However, like I said, for 99.99999% of cases, it's not even remotely feasible. And for THIS particular socket, might not even be POSSIBLE.
LGA 771 is circa 2006, and not worth anything, really, to anybody anyhow. Possibly in some lesser developed regions, but honestly it is really not able to run much if anything when it comes to modern OS and software anyhow so unless somebody is only interested in running old operating systems or programs it's probably not very tempting.