Hmmmm tough one.
Legally, if they overpay you - do you have to return the money?
I was overpaid once, I don't recall exactly how much but it would have only been a hundred dollars or so. I never noticed the extra cash in my account but my employer realised they had made a mistake and told me about it. They never asked me to return the money (nor did they dock it from future pay). I certainly never offered to return it, either - I figured it was their mistake, not mine. $100 is quite different to $12,000 though, LOL.
If I got overpaid I probably wouldn't notice it (at least for a while, anyway). My partner and I both have our pay deposited directly into our mortgage account and we rarely check it, other than a quick once-over of our pay slips when we receive them.