I can share my experience as a candidate who received a kind, but ultimately unclear quasi-rejection after my campus visit.
What had been done well: On my visit, which was about 7 days after a Skype interview, I was told that another candidate was coming on X day and that the faculty would meet to make decisions around Y day and I'd hear from them shortly thereafter.
So sometime around Y day, I get an email from Department Chair.
I told you that I would keep you informed about our process, so I am writing to let you know that our search committee voted yesterday and decided to pursue another candidate, and the rest of the faculty has endorsed that decision. I know this is not the news you hoped for, and I still greatly appreciate the time and effort you spent as part of this process.
You will not receive any official notification for quite a while because those do not go out until after someone has formally accepted the position.
This note was consistent with the kind and high-integrity people I dealt with there. Indeed there was a lot of effort put into the visit and they knew I had a deep personal connection with the institution.
Knowing how faculty searches work, and given what had been communicated to me previously, this note was consistent with two potential realities:
I was still under consideration but ranked below another visitor.
I was excluded from further consideration and should regard the email as a rejection.
Obviously a common tactic for search committees in these situations is to not say anything to the lower-ranked, but still hire-worthy, candidate(s) while you negotiate with the top choice — this would go along with interpretation 2. But my previous communications with the search committee made the "keep lower-ranked candidate in the dark" strategy untenable because they had promised a follow-up at a fairly specific time. They had to tell me something at that stage.
The final sentence led my mentors and I to conclude that it was likely, but not certain, that I had been excluded from consideration. On the other hand, it may have been included just so I wouldn't be blindsided by an automated email later on if the top choice indeed accepted the offer. Normally you can never know which interpretation is correct when I was ultimately not offered the position, since either one is consistent with my not getting the offer.
In this case, I later learned who the other candidate who visited after me was. This candidate was also not offered the position and received a similar/same note at the same time. We are quite confident, though not 100% certain, that at the time we received this note that no other candidate had visited and the timelines involved allowed for no more than 1 other candidate.
A couple months later, the department announced they had hired 2 candidates for that position. This leads me to conclude that they likely brought just 2 initial candidates on a visit (the other person I know and me), we were both found unacceptable, and they subsequently brought additional candidates to campus and later decided to offer at least 2 of those.
My recommendation: If a candidate has been eliminated from consideration, please make that clear. The other information I would later get about the process leads me to believe that when I received this note, which did not explicitly reject me, I had already been ruled out as a viable candidate. I suspect the Department Chair intended me to get that message, but did not word the note carefully enough, perhaps due to an effort to soften the blow. I don't know that I needed/wanted to hear the gory details (e.g., we were sufficiently unimpressed with you after your visit that we had to extend our search process beyond its initial plan just to get somebody we could hire) but certainly I would have benefited from not hanging on to a bit of hope when it later became clear that I was wrong to do so.
I and the other candidate waited in limbo, unsure whether an offer might be forthcoming, until seeing Twitter announcements from the 2 who received the job. If I hadn't seen those announcements (or if it took another couple weeks), the possibility of a forthcoming offer could have affected negotiations I had with another institution.
Aside: I was fine receiving this information via email. In fact, I'm glad I did rather than in a phone call. Such a conversation would be awkward, especially given the emotions involved. That being said, I'm mildly phone-phobic so there's not a lot that I like to do over the phone.