Not in my experience... The last three companies I've been with have either gone under or been bought and sold off (yes, it sucks to be ME!!) and the CEO took no blame at all in any case. In fact every one of them moved on to similar or better positions at similar or larger companies. Primarily because they were gone before disaster set in.
In my opinion that's why you see so many 4 year CEO's now. They come in, raise the stock price by any means necessary (layoffs, cut backs, no overtime pay but no schedule cuts, cut everything to the bone), and skedaddle before the chickens come home to roost. You can bring about short term gains in market price pretty easily if you don't care about the long term viability of the company and that seems to be the game I've seen several times. Not always the case of course but it's not uncommon.
My personal view is that CEO's should have more liability in their contracts concerning the long term viability of the company's they run. But, of course, boards of directors are usually made up of CEO's from other companies and they don't want that liability on them so they're not likely to ask for it on anyone else....