That's a micromanaging board, and no CEO should put up with that because as the most public face of a company it'll make the CEO look far worse than "the board". But OK, she's getting paid a metric f ton of money so maybe she doesn't care how bad the boards' micromanaging makes her look.
The longer she can ride the gravy train the better for her.
So she probably will do whatever the board decides that week.
(The Board):"Let's have more cuts" (Her):"Ok". (The Board):"We should buy a startup" (Her):"Ok."
I can't believe she doesn't know or nobody told her the ship is sinking (or the gravy train is headed to a dead end). She knows it. But yeah as you said, at this point she is just playing the game of "let's see how long I can hang on here".
In the end she can point fingers to "the board", "internal naysayers", "it wasn't much that could be done", etc, etc. The board can point to her. Employees and customers will point to both and so on.
