It's a cashless loan. If you have options that cost $10,000 to exercise, the company lets you pay with a promissory note (promising to pay the $10,000, plus minimal interest set at the IRS's AFR). This is effectively the same as the company loaning you $10k, and then you hand it back over to exercise, but the cash does not change hands.

If you were to get a private loan, the interest would be much higher.

The company does not want to be in the business of making loans, but this is a way to allow the employee to exercise upfront (and thus potentially get certain benefits, like in a good exit scenario, of having gains be subject to LTCG and not ordinary income), in the best way possible. But in a downside scenario, like the company folding, the person is on the hook for the loan just like if they had decided to exercise with their own money.

Re: last paragraph

Is it realistic for a bankruptcy trustee to come after employees that signed uo for a personal loan for shares in a company now worth zero.

Is there a documented case of this happening and suceeding?

In that Twitter thread where the CEO originally announced the idea many people reported this happened in the dot-com bust. Private equity firms would buy the company and go after past employees for the loaned money.