If the liquidity is enough,
1) Short Bitcoin to the tune of several Billion dollars.
2) Do a 51% attack and essentially prove it's worthlessness.
3) Profit
If you have amassed enough hashpower to be able to do the 51% attack you have far more to gain economically from continuing to mine for the network than to somehow short it (impossible to find a counterparty for a transaction that large) and then have billions of dollars of hardware that is now worthless
Also if multiple parties attempt to mount a 51% attack then they will have to compete with each other which makes the attack impossible.
Are the sort of places willing to sell options on BTC the sort of places that would honor such a contract if the price went to 0?
Such is Bitcoin's continuing rediscovery of all of finance, now including the 2008 Global Financial Crisis.
Contracts are established between market participants; the issuer is just a facilitator. LedgerX options are fully collateralized so you could certainly reap the entire value if you bought a put and the price dropped to 0. Liquidity is not very deep though, so you wouldn’t be able to buy much. Margined products (such as Deribit’s options) would probably be force-closed long before the price hit 0.
I feel like LedgerX bragging that they are both an exchange and a clearing house does not inspire confidence in their risk management department, although I'm sure the bright minds at the SEC have done their due diligence as they always do.