Not sure about the details of shorting a delisted stock, but I imagine if the stock ceases to exist you logically have no obligation to pay anything back (i.e. cover the short) since the stock is worthless.
Regarding puts, I am sitting on NEW puts right now so I’ll find out soon what the procedures are. However, I was assured by my broker that if the stock is delisted or essentially worthless, the seller of the “put” contract is still under obligation to pay the money which would essentially be the entire strike price at this point.
