A few years ago, when dirty furriners upon entering the USA still got that little tourist visa coupon (I-94W Departure Card) stapled to their passports, which was removed by the airline staff at the gate desk while leaving the USA, my coupon was not removed. I noticed that mistake several months after returning to Switzerland. From the legal point of view of the US immigration authorities, I was an overstay, although I had left the country.
There is a little office in London, Kentucky, that deals with such cases. At that point in time, all it had was a P.O. box address, no street address, let alone a phone number, fax number or email address. I was asked to send them evidence of my presence in Switzerland, such as boarding passes (who keeps them?), wage slips (I'm self employed), a Swiss immigration stamp in my passport (I'm Swiss, so I didn't get any), signed bank checks (nobody uses checks in Switzerland, it's sooo medieval) -- the whole list of possible documents didn't apply to my case.
The guys in Kentucky usually needed eight weeks to answer one of my letters, and express was mail impossible, because that needs a street address. In summer, the time for my next trip to the USA was running out. A friend of mine in Michigan, a famous journalist, suggested to ask the regional Representative on the Hill for help. And that helped indeed. Within ten days, my next entry to the USA was cleared. Without that, I would have been arrested on the spot and put in the next plane leaving the country, no matter what the destination was. Seriously.
That's bureaucracy at its best. And now the USA even demand payment of kind of an entrance fee for tourist, saying the profit is used for promoting tourism. That's like to promote virginity.
Swiss authorities handle overstays fairly strictly, which, in my opinion, is a necessity to prevent abuse, but they are humans too. My American OH recently had an issue, an overstay of one day due to a canceled flight. A brief call to the Federal Immagration Office in Bern solved the case within minutes, and other than a somewhat-longer-than-usual look of the guy in the passport booth at the monitor after scanning her passport, there was no problem.