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.
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.
How often is margin calculation done? And what is the time period allowed for option sellers to cover their margin?
Also, what happens if my counterparty can't pay? Is the exchange going to step in and guarantee the trade?