There's 10 ways for you to get devalued to 0 and you have to avoid all of them to make a payout.
In fact: for this reason, I'd be especially wary of companies trying to buy a few thousand dollars of annual fully loaded cost with large amounts of equity --- it suggests extreme naivete.
In the life of every company there is a moment when there is not enough money to hire the next two people, but there is also a feeling that hiring those two people would take the company to the next stage so much faster as to make the hiring worthwhile. At that point you either raise more money directly from investors, or offer more equity to prospect employees, or hold back on the growth.
Raising extra money takes time, so it may not fit with the timing of things. Holding back should probably be preferential to giving away equity, however somethings growth is unusually important, for example when you're in the middle of a land-grab.
She had rejected his salary + equity offer which was a %50 salary cut from her current position.
Irrespective of what the equity portion was I thought the founder's response was disgusting and pretty much validated her decision to pass.
That's why they are trying to pay you with them. For them it's a one-way bet. It's sadly just another case of pushing risk onto the worker and not really passing on much of the upside.