Suppose BTC drops 40% in value or $60 in one month, now the notional value of my BTC contract should be $40/BTC or $4,000/contract. Not only does 20 BTC valued at the original value of $2,000 no longer cover the mark-to-market value of my put contract, its market value at $1,200 covers even less that requirement.
Now suppose I'm nervous because I'm sitting on a contract that should be worth 4K when the collateral of my counterparty is only worth 1.2K. Also since I bought a put which means that I'm betting against BTC, that would only make me more nervous about counter-party risk; and I'd demand my counter-party to put up more collateral.
However, if the exchange isn't willing to extract from my counter-party and isn't willing to step in. Then, I have no confidence in such a market.
If your counterparty can't pay, then you get the full value of their margin account for that trade (plus the premium payment, which you already received) and no more.