I did a search for `startup "put option"` to see if there was anything written about this. There is one article arguing that major early investors should demand something vaguely similar [1] -- although it sounds like it is not designed to be triggered when a company fails and loses a lot of value, but instead perhaps when a company is partially succeeding, or succeeding but the investor wants to reduce exposure or otherwise get some cash back:
> If the investor exercises the put, the investor is entitled to redeem all or a portion of his equity interests in exchange for the initial investment value plus a nominal return above the risk-free rate, yet still maintain a reduced equity position in the company–perhaps, somewhere between 50% to 75%.
> To prevent the investor from exercising the put at a moment when the company’s financial stability or expansion plans could be jeopardized, the company can require that in addition to a prescribed time period restriction, certain revenue milestones must be achieved and set as “triggers” before the put may be exercised.
> The put option must be structured in a way that enhances the investor’s optionality without putting the company at balance-sheet risk. It is possible to strike that balance.
[1] https://www.thinkadvisor.com/2010/04/01/venture-populist-the...
Another variation would be to strike a deal where put options were not written by the startup but by some other third party (an insurer or bank?), which was highly likely to remain liquid in the event that the startup went bust. This could avoid needing to constrain the use of the options with triggers & so on. On the other hand, it would be a pretty risky business for a third party to sell such things, so they probably wouldn't be cheap to buy...