If an HOA successfully forecloses on a condo owner do they have to sell the condo at auction or can they cut a private deal?

It goes to auction.  They can't just sell it, and here’s why – the association isn’t the owner just by virtue of a foreclosure judgment.  When they foreclose on the property, the judge orders a sale.  Ownership doesn’t just transfer to them.  The Court holds a sale and the highest bidder buys it at least for the judgment amount (lien, plus attorney’s fees and costs usually).  Now, many times, there’s no bidder so the condo or homeowner’s association buys it so they can sell it.  So, long short – if you want to purchase a foreclosed condo, start with the auction.  Keep in mind, though, that even if you get it for a “steal” like five or ten thousand, it may still have liens like a bank loan on there and they can still foreclose – it’s a messy situation that’s become more frequent with the crisis in FL.