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.
Such is Bitcoin's continuing rediscovery of all of finance, now including the 2008 Global Financial Crisis.