Even if they don't "lose" their equity, it might just turn essentially worthless. Very often "equity" founding staff receives is in the form of (V)ESOP s = (virtual) employee stock options, or other equity grants that only materialize in the case of an "exit event". Depending on how the exit events are specified in the contract, the founder taking the company private (/ divestment from the investors) might have resulted in an exit event with $1 value of the company.
Yeah so pure grift : if it was really dying then just keep your worthless-percent forever, or get emotionally manipulated into selling for $1 like a sucker