The latter! I was departing from Lanzarote back to Stansted last November, and (IIRC) the passport control booths are by the gate(s) for the non-Schengen flights and they were non-staffed. Somehow you only go past them once you start boarding, so at that point it was too late to go back and start looking for some (National) police elsewhere. I asked the gate agent and she just shrugged.

I haven't helped the situation by having two passports and entering the Schengen area using a different one instead of that I had in my flight booking/APIS (UK). As I've then entered back in the UK on the UK passport I have no stamp there either. Although, I've managed to get an (exit) stamp from Serbia few days later.

Then to make things worse, couple of months later I was going to Spain again, but the first passport didn't have sufficient validity before expiry, so I had to enter using the UK one. I tried speaking to the police on entry and exit (got stamped both times on that occasion), but the language barrier was too great. One of them just said to speak to Lanzarote police...

So, technically, I think I am still "in Schengen" and overstayed by quite a bit... I am going to Finland in couple of weeks time and I might try explaining there and seeing if they have any suggestions how to rectify this. Will bring all the passports and boarding passes.