Do what I do.
I've been through downturns before and the secret is just to keep publishing but to keep publishing better quality content.
I know that's not the answer a lot of people are looking for.
Most people would rather have some sort of magic bullet one-size-fits-all quick solution.
Unfortunately, that's not the world we live in today.
That may have worked a decade ago but given how Google is evolving, if you are a completely white-hat operator and you don't use any black hat techniques, this is the only way to go.
Keep publishing content but make sure that you're not just publishing content for the sake of publishing content.
Don't just go through the motions.
You have to produce content that actually delivers on the search intent behind the keywords that you're targeting.
Otherwise you're just wasting your time.
It also helps tremendously if the new content that you are publishing naturally links to the content that got demolished by the recent update.
What I mean by ‘naturally links’ is that the value of the content on the page that you are linking from is actually enhanced by the value of the page you're linking to.
Do you see how this works?
It's all about value linking.
Unfortunately, a lot of online publishers focus solely on SEO.
This is a big mistake.
Remember Google's customer and your customer are one and the same.
You should both be looking out for the best interest of your website visitor.
Take care of that and Google will take care of you.
It may not happen overnight but it will eventually happen because most people refuse to do this because they are looking for quick and easy solutions.