I already posted my experience from 2008 somewhere else for anyone concerned about a recession. No two crises are equal, but might give you some pointers.
My personal perception of the 2008 wreck is the following: a some people got royally screwed, many people got screwed, some people didn't feel a difference, and a few people actually thrive. I was in the second category.
First, my company imposed a hiring freeze. This included both hiring new people or renovating temporary contracts. Then, they relied in natural attrition to shed people. Since many people were contractors, those were the first ones to let go. When that wasn't enough, they started laying off full time employees.
I was lucky since my team was left mostly untouched, while other teams were dismissed entirely. We did get our bonuses cancelled and salary frozen for a few years, however. That, coupled to higher taxes and inflation, means that my income went down over the years, but at least I had a job.
My biggest takeaway is that YMMV (duh!). Many people are concerned now about losing their jobs. In my opinion, companies (particularly large and stable ones) will rely on hiring freezes and attrition to curb their numbers. If it comes down to it, you are more likely to see teams being fired wholesale rather than each team bleeding a bit.