Personally not in this situation but if anyone is in the interesting position of owning puts in the two banks that went bust its quite interesting to see what happens now that trading is suspended. Basically you cant close your puts but are forced to exercise them, I recall a ticker of some years ago that went bust and people had to exercise only to find that trading didnt resume at all. So they were forced for months or even a year to pay lending fees for the short shares which eventually ate up all their profit from the put position.
Its interesting that for the two banks the document out appears identical:
https://infomemo.theocc.com/infomemo/search
I attached the specific notices to the post - note that these were downloaded today and may be subject to change so the main link above should be your reference. What is interesting is that the notices say that the OOC may decide to go for cash settlement which would be good for put holders. What I saw on other boards is that it is recommended to wait with exercise (if you can - the first expiry is this Friday) until the day of your expiry or if/when the stocks start trading on the pink sheets. At that moment you could exercise your puts (presuming you didnt hold the shares) at your leisure though its not guaranteed they trade for zero.
It always seem like an option trader dream to have a put on a company whose value goes to zero but in practice its actually complicated, those selling calls are better off!
SBNY notice.pdf
SIVB notice.pdf