All it takes, for example, is a medical tragedy to befall you or your close family - medical costs are one of the biggest reasons for bankruptcy as now insurance companies play fast and loose with who, what and how much they cover.
A side-effect of having a year's living expenses saved up is that you have a measure of self-insurance against medical or legal misfortune. Combined with catastrophic health coverage, this makes it possible to weather even a fairly bad storm.
Beware of believing the party line on medical bills and bankruptcy, by the way. As far as I can tell, surveys showing that medical bills "contribute" to a large fraction of bankruptcies fail to establish causation. What they do show is that people who declare bankruptcy also often have significant medical bills. But of course many people do. I bet lots of people who declare bankruptcy also have car payments, maintenance, and repair bills, but it would be misleading to conclude that car costs are one of the biggest contributors to bankruptcy. Since no one is (yet) advocating for "national car coverage", the political motives are different.
See, e.g., http://content.healthaffairs.org/content/25/2/w74.long for more information.
It's typical for a family of 4 to have 2 new car payments, tens (if not hundreds) of thousands in student loan debt, a $300K mortgage, $20K or more in credit card debt, and all the costs of kids (soccer dues, etc). How long can a family like that do without income or at best lose half? Probably 2-3 months, tops. That's what causes bankruptcy.
It sucks to lose your job, but there's a simple and time-honored solution to this problem: savings. It's amazing how much less you're pushed around by life when you have a year's living expenses in the bank. (It's also amazing how fast you can accumulate such a cash hoard when you consistently live below your means.)