I did the same last month. I was pressed for a number in the in-person interview. I dropped my inflated public number (which was $30k more than my walkaway), and lo and behold, they offered it to me!
Heh, I'll see your met offer and raise you a....um, raised, offer?
Was asked a couple of weeks ago what my number was, gave them what I was making in the market I had just moved from because I'm a single guy with a cat and can get by very easily on that and still live very comfortably.
They added an extra 25%. Ten short of the public inflated number.
In my experience it really isn't that rare. There are a lot of people who do not job-hop nearly enough to optimize income (maybe they're optimizing for stability though, that's their business) and once they've made one jump there's such a possibility/probability of doing so again that it's not really in an employer's best interests to make it easier for them to do so by taking advantage.
Most engineers only reach their steady-state productivity 9-12 months into a new job. Getting a year of somebody cheap is rarely better than getting multiple years of them unless you never should have hired them at all.
Not unusual if the hiring manager is at all experienced.
I MUST keep 15% or so in my pocket if I can. There are some people that simply will NOT feel good if the don't negotiate with you. Shrug. I let them "negotiate" their 15%.
To the ones who don't negotiate, I put the 15% into their final offer to sign.
I got $10k on top of what I was asking for. I undervalued myself quite seriously as I was moving countries and didn't really have a good grasp on what market salaries actually were for my experience and skills.
It may seem smart in the short run to hire someone for under their market rate, but when they eventually realise that they're massively underpaid, they're going to jump ship.
It turns out I was way undervalued :)