I think I've been scammed, but it's weird. What would be the scam here?

I saw a job ad for a software engineer in my area; I've moved around a fair bit so I'm having trouble finding work, and I wasn't too surprised to see that the company of the job ad didn't exist in my town though they do seem to have an office in a couple of major cities.<br><br>I decided to give it a go anyway. I think on the assumption that the job might be from someone I know, or maybe the company was expanding to my town. The job wasn't on LinkedIn or any of the other major job boards, I think I found it on indeed. If I knew then what I know now I would have never applied, but here I am.<br><br>The interview process is super weird though:<br><br>- The return email was what looked like a content moderator from linkedin. - So this was my first clue that the job wasn't real, I figured the return email was likely linkedin's attempt at automating a response though, so I decided to keep going.<br><br>- The email was from a generic "HR Jobs" email account; I went ahead and responded, because HR sometimes do that anyway. So I figured the real company just hadn't set up their email yet.<br><br>- A few hours later, I got a response from the "HR Jobs" account, asking me for more information about my past work. I sent that information, and got a response a few hours on asking for some background information for a background check. At this point I was certain that it must be a scam to get my SSN, but they also included a briefcase icon in the email body, and the return email address was moved to the company email domain. I figured it was more likely at this point that the "HR Jobs" account was an anti-phishing account, and the response was automated when it determined my email was safe enough to risk sending mail from the company domain. I decided to put a fake SSN in, and decided to go ahead anyway.<br><br>- The next response came shortly after, from the company domain, and it was the company email address. So at this point I figured that the process was just going through different people. The email spoke as if I had already taken the background check, even though I had only put in a fake SSN, and they just assumed I got it right. This email contained more information about the background check. I read it, filled out a couple of questionnaires, and sent them the results. I still think at this point that this is a real job, and the company is so big that they have to go through a lot of hoops to make sure they're following all the rules for hiring. I figured that if I was in the position of HR, I would almost certainly do the same thing, given that it means you can't be held accountable if you turned down someone for a discriminatory reason because you already know the discriminatory information before you review the application.<br><br>- The next email response was basically them pointing out that my SSN was fake, and they're going to cancel the job ad. I'm not too excited to go back through and find it, but I think the wording of the email was along the lines of "You have failed the background check, and we have decided not to proceed further with your application, we're going to cancel the job ad on your city as soon as possible". I mean, I get it. I write software for a living, but I'm definitely not an expert in linguistics, so I'm not positive this is exactly the wording they used, but you get the idea; the job ad was for my city, and they're going to cancel the ad for my city soon. Not the entire job ad. By this time I'm thinking the job ad is definitely fake, and to be careful. My money was on the scam being to try to steal my SSN, but it wasn't working because I put in a fake one.<br><br>- I got another email a couple of days later, and the wording on this one stuck out to me, but I think they said something like "We cancelled the job ad; If you see the job ad for [City] then it is being placed by a scammer, and is not linked to our company". First off, the job ad is still up. And second, they're now saying that the job ad is definitely fake? Or, at the very least, that any job ad for my city is fake?<br><br>I'm still playing around with it, I'm not at all put off from the company at this point. In fact, I'm extremely excited about the possibility of working there. I mean, they decided *not* to cancel the entire job ad, they said they're only cancelling the job ad for my city. And they didn't cancel it, so I can still apply. I'm thinking at this point that I've somehow been moved to the special hiring process.<br><br>Here are a few thoughts that I have:<br><br>- They could be saying that the job ad is fake, and that they're cancelling it, but what they're actually doing is cancelling any job ad for the city for anyone that isn't me. This seems like a lot of work, but I'm not going to write it off entirely. Maybe this is what's going on, and I'm just the chosen one.<br><br>- They could be trying to use the job ad to collect a list of people who put in fake SSN's, and then they use that list to build a list of people who may be linked to identity theft. This would explain why they left the job ad up in my city, but I think they said it was cancelled in the other cities as well. I think at this point they moved the job ad to a different website. This also doesn't really make sense, because they put the job ad up in the first place. So they already know who is putting in fake SSN's.<br><br>- I think the weirdest thing about this is that they're still sending me emails. They have literally said "We're not going to hire you, please don't contact us". And I'm still getting emails, both automated and what appears to be human. This is the most confusing part of it all to me. They've explicitly said they're not going to hire me. I'm confused as to why they're still emailing me, and what on earth they're trying to accomplish. They have said they are not going to hire me, but they still seem to be trying to hire me.<br><br>Does anyone have any ideas? I've never heard of any scam like this, but then again I've never been in this situation before.<br><br>&#x200B;<br><br>EDIT: Wow, I didn't expect this post to blow up at all, but I appreciate the feedback. My current stance is to just keep playing along, see where it goes. I'll update if anything new happens.