Because you engage them. Well done. Even if they don't convert today, you have built up good will. And wasn't that easy?

In answer to OP, I'm eager to see the responses. A simple error document that is mapped server-side to read the correct message makes as much sense to me as anything else. We should have a link to the site map, and the home page, and in some circumstances a link to the their last page (non-dom). I don't offer much else. It's an error page, so one should want to be out of there pronto. Better they dwell on the site where they'll find what they came for.