Unless there is another job offering with similar compensation/benefits/etc. I'm not sure most employees will be able to do anything. "Leaders" and bold-faced lies are a duo as old as time. Macroeconomic conditions have many chained to their shitty bosses.
Hmm, I think I trust that my CEO isn’t lying to me. It’s just that he isn’t ultimately in control. If he says something and the board changes their minds the day after, he’s stuck.