I assume that this means you're sending out rejections that include a mention of "we've hired someone else for this role".
If your hiring model is hiring multiple people through one posting, then you will probably get a lot fewer angry ex-candidates being weird (because they think you've lied to them since the posting is still up) by just sending out rejections that don't say that and just get the "we're no longer interested in you for this role" message across.
Nicer/more corporate language for both, of course.
From applying places recently I'd much rather get these fast. One company sent me them, the rest either reached out or I never heard from them.
> I assume that this means you're sending out rejections that include a mention of "we've hired someone else for this role".
No, this isn't possible unless you delay rejections letters until you hire someone.
We send letters as soon as the decision is made not to continue with that candidate.
Honestly it would be cruel to string them along any longer.