Good CEOs don't need to work for failing companies. A failing company is a lot of work to make successful, or even just to fail less hard. If their compensation was based on how well the company they run does then good CEOs would want to work for companies that are already doing great, concentrating their skills on companies that don't need them as much.

The Board of a failing company needs a good CEO. A good CEO might be able to save the company, and it doesn't really matter how much money you save if the company continues on a downward spiral ending ultimately in their going out of business. But you aren't going to attract a lot of talented CEOs by offering them a crappy job with a relatively low chance of success while only promising to pay them a bunch if they succeed.

CEOs generally have their pay composed of two parts: A baseline pay they get no matter what, and additional tiers of compensation for if they do well. For example a company might expect 5% growth and agree to pay the CEO a certain amount, but if the CEO can get more than 5% up to 10% growth they get a bonus, and if they can exceed 10% they get a huge bonus!

In the case of a successful company a CEO might be willing to accept a lower base pay because they think it is more likely they can get those extra bonuses. But in the case of a failing company those bonuses are probably much less likely to obtain so the CEO will want a higher base pay (since that is likely all they will get). The offered bonuses might be higher too considering if they can take a company losing money and grow it 5% then it is way more of an accomplishment than the company that did that normally.

Finally, just because a CEO doesn't succeed in saving a company doesn't necessarily mean they are a bad CEO. Turning a company around isn't a guarantee, and there are even ways of relatively gracefully managing the failure of a company such that shareholders lose less money than they otherwise might. This is why a CEO might preside over a company going under and then be hired away by another company wanting their talents.