Back in August 2012 Google released their DMCA algorithm penalty, also known as the Google Pirate penalty. It basically looked to downgrade site's rankings where those sites received a large amount of real DMCA complaints. As far as I know, they updated the algorithm once in October 2014.
Since then, no one really talks much about it. Google probably doesn't refresh it and sites hit by it probably are stuck worse than those hit by Penguin.
That being said, Google spam fighter Eric Kuan gave some advice in a Google Webmaster Help forum related to it. Let me quote him:
A few more tips that might be helpful for you. If you think that your site is affected by a particular algorithmic adjustment, I think it’s worth the time to continue rooting out and removing these types of sites. Separating your main domain from the user generated content on your site will also be helpful since you can’t always control what users put on their site.
If you’ve made significant changes to your site, note that bigger changes can take time to settle down. Also, keep in mind that a lot of things can change over the years and your site’s ranking and performance metrics can change over the years.
It looks like you’re moving in a good direction, though, and continuing these good practices on your site will definitely be beneficial for your users.
The sad part, it seems like it can take a really long long time for any site to recover because algorithms need to be refreshed, I think at least this one does.
I've only heard of a handful of sites impacted by this update and I think most of those abandoned the sites to do other things.
Forum discussion at Google Webmaster Help.