We started doing this in late 2014. There's an explanation at https://news.ycombinator.com/item?id=11662380, with links back to others. We've talked about it in comments and whatnot (https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que..., https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...), and have intended to publish the list, but only did so recently. We're slow.
If you see a submission that didn't get attention and which you think is particularly good for HN, please tell us at hn@ycombinator.com! We love getting those requests and usually add them to the pool. It's fine if it's your own article, but we like it better when it's just something you ran across and recognized as good. That's more the kind of interest that HN is for.
A related list is https://news.ycombinator.com/invited. Those are old submissions that we ran across and thought deserved attention, so we emailed and asked the submitter to repost it. Yesterday's top story was one of these (https://news.ycombinator.com/item?id=26982286). They all go into the second-chance pool, but maybe it's interesting to see them broken out as a subset too. (If you don't have an email address in your profile, please put one in so we can send you repost invites!)
If you read the old explanations I linked to, you'll see that the original plan was to turn this system into software that anyone can participate in, likely as a new way to earn karma: users who discover second-chance links that hit the jackpot (that is, which interest the community) would get karma along with the original submitter. That is still the plan! We're just slow.
I think that's about everything there is to say about the second-chance pool. Questions, feedback, ideas, and views are welcome as ever. And please, everybody keep an eye out for obscure, out-of-the-way stories that got overlooked and let us know when you run across them. It's one of the best things you can do to help make this place more interesting. Best of all are the kind that can't be predicted from any existing sequence: https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sor....