I've had it happen a few times. Most recently a company told me at the time that they were impressed but it would've been a waste of my time and skillset to take the role they were hiring for (VP at BigCo). About a year later they reached out with a generous offer for a role they had created specifically for me, which genuinely was a better fit.
I've been on the other side of that conversation as well. It usually happens when someone really impresses and stands out but doesn't actually match what the role requires. If you have a limited hiring budget, you can't always squeeze in a person you'd love to hire in addition to someone that fills the critical role. Smart companies will invent a role for great talent, if they can make the budget work, but that often takes a lot of time to put together.
I was talking to a friend last week who got hired this way (initial rejection, then a position opened up that seemed a better fit). It does happen, I guess.
In my experience from the hiring side we never call back people but very often shuffle promising candidates between different roles. Like we are interviewing people because we need a Foo-guru and one candidate is kinda meh in Foo but shows promise as a Baz-person then we for sure let both the person and our recruiters and the Baz team know. And our team receives similar referals from other teams in the company too.
Very Jr role. Hiring manager had a very specific role that the recruiter got me on. Rejected, but during the interview pushed me to the next round of a lesser role in his team.
Recruiter was pretty amazed at the turn around since it closed so quickly.
It's a hard job and everyone at my level is a skill a notch or two up and much younger. But we do what we can to stay fit in the industry when peers are much more experienced and sharp. I got my foot in the door. It will take a lot of effort to shake off the sunk cost of training and replacement of me so I am here to get paid to learn and soak up what I can. Definitely high work load and high turnover either upwards or outwards for better opportunities
So if they have a budget, especially if they are a vendor with a paying client who needs a minimum level assigned consultant headcount type of metrics, I am good enough and my soft skills push me through.
Previous job (hired 5-6 years ago) I actually asked to be considered for the level above the one I originally applied to as they pulled me in for interviews. They hired me that week for the tech role as they likely had worse matches until I showed up.
You can't have a full strategy around it. But when you see a possible opportunity you snipe for it. Take the minimum amount of effort and just enough to set you apart and it might just be enough. It's a draw attention to yourself and make it feel like they won't find a better candidate. Play the fog of uncertainty every desperate employer has. Desperation can come from Recruiter delaying the first round because busy with a more important leadership fill, or low recruiter count in general, bad recruiter giving bad leads, etc.
Similar opportunities to me is sometimes just being the first result in a employer's search. engine.
I want to be optimistic. But realistically, how often does that actually happen, even in this hot market?