During the 2000 and 2008 crises, there were massive layoffs, which impacted contractors just as they did employees.
In 2008, I contracted via an IT outsourcing company, and every week there was another announcement about a batch of colleagues being laid off. The firm's clients were canceling projects, and having consultants on the bench is very expensive.
Who knows what this will look like, though. If it ends up being like 2008 and clients start canceling projects, then yeah, it will get tough.
Not sure if I can give any generic insights on how to handle the down market as a contractor. A strategy that will work for you depends on your existing skills, niche, and network. As well as your appetite for risk.
If my appetite for risk were low, I would stick to my corporate "whale client" and ride out the recession on whatever boring project they've been running. I've done this during COVID.
But, a recession might also be a great opportunity to try something new. If what you do can translate into reduced costs for your clients (e.g., you know how to bring AWS costs down significantly), that type of expertise is very valuable when CFOs are slashing budgets).