Don't care who you are... Nobody is worth that much a signing bonus
Let's say you are CEO of a retail company. You turned it around from a declining company into a profitable one, establishing your reputation as capable of managing a retail company.
You are literally the boss of the entire company. You can stay there and reap the benefits, collect your unvested stock grants and stock options, and probably receive more. You're set for life.
Another company offers you a job, albeit as a Senior Vice President. It's technically a demotion, but at a much larger company where the stakes are higher. You will be required to make decisions and direct strategy that can add (or subtract) hundreds of millions to the company's bottom line, each year.
If you succeed, you might get a promotion to a C-level position again. If you fail, you'll fail spectacularly. No one will ever hire you for a similar job -- even if the reason for your failure is out of your control (product problems, poor economy, a superior competitor).
What would it take for you to leave your current position? And, if you are willing to leave your CEO post, you are likely talking to more than one company -- including ones that are offering you a CEO position. What do you think they would offer?
From the company's point of view: they are hiring someone to make decisions and direct strategy that can add hundreds of millions to the bottom line each year. If she can do it, 10's of millions per year in compensation is is a fraction of the potential payback for the company -- and a great return on investment.
Wouldn't you invest in a stock if you were reasonably sure you would get a 10X return?