First fully expired domains that are not even indexed.
Benefit is low price (cost of registration) high reward - organic link juice.
Downside is if its not indexed you don't know if its DEindexed
(penalized) or will never be indexed again. If that happens your $9-$12 is flushed won the toilet.
What you look for?
Wayback machine is key so you can see what the site last looked like. Extra tip though is if you are going to be buying a bunch of these you would do well to get a subscription over at Domain tools. Why? They are one of the few places you can get historical whois data. That data will tell you when the domain changed hands. If it never did then it was less likely to have been deindexed (almost certainly did not)and when you set it up again it will return to Google results. DT doesn't make sense for few domain purchases because its $49 a month plus you don't get unlimited whois histories so you would use it only when a domain really intrigues you and Wayback isn't telling you enough
As far as Wayback machine - It misses a whole lot of snapshots for domains so it missing a year or two doesn't mean much either way however if the last snapshot was a legit site and its been many years I take the chance quite often. its the cost of registration and some misses are a part of the equation. Now if you combine that (on what you think might be a special domain) with whois history from Domain Tools and see no one has registered it since the snapshot you have a winner.
I won't get into how to find fully the expired domains with good links (I don't use the "Hayden Method") since thats self defeating to share on an open forum but in regard to link checking - I gather some people are not checking backlinks because of costs for ahrefs etc. Seokicks/Moz/blekko are good free backlink checkers that if combined pick up a lot (and if you have some cash Backlink miner combines into one)
For Both auctions and expired domains -
I see A LOT of people STILL are mistaking the use of metrics - whether its PR , DA, Trustflow or whatever. The only purpose of metrics is to tell you what domains to look at more closely and run backlink checks on - THATS IT. They are not signs that you should buy the domain only that you might want to check the backlinks
You don't buy on metrics and you need not spend time wondering "but why does it have a DA of...." None of the metrics are even close to perfect. Its been said over and over again that you buy domains for links not PR or DA or trustflow but I think the confusion exists because people do not understand how the metrics fit in.
They basically just save you from having to check the backlinks on all domains available. They should be used as filters
Finally no racsim or nationalism but its just a fact that some areas have more spammy sites than others. The number one for this is China just from the sheer amount of people from there. I avoid domains from there most of the time because they have a higher rate of being deindexed. Compounding that fact is that if you don't speak the language its even harder for you to avoid bad domains.
Just a couple tips. Happy hunting