Yes...the Coop does have a duty to maintain certain standards like minimum price per share but most Sponsors wont just drop or dump their units one at a time. Typically the sponsors will figure out a way to sale the entire package. I have been involved in half a dozen (or so) estate sales with Coops. Most people are afraid to reach out to a Board. An approach is very simple...CASH BUYER (Now, now - Please don't say there are no cash buyers out there...66% to 70% of my sales are to cash buyer)
First, you educate the executor and possibly their attorney (yes, most lawyers are NOT COOP savvy). You agree on a "fire sale" price but it must be for a cash buyer (BANKS WILL ONLY ALLOW ABOUT 6% concession, SO THE FOLLOWING APPROACH WONT WORK) . Example...if the average price for a similar unit is $200k, you may want to agree to dump the unit for $150k Cash (if the market is bad). Then you have the executor and the attorney reach out to the management and the Coops lawyer. They explain the perilous situation the family is going through and humbly ask that they be as flexible with a buyer as possible. They introduce the listing Broker and the he / she promises to get a minimum price for the unit and you put it out to market FOR CASH BUYERS ONLY. Keep the Unit off the MLS and use every other source...including your local brokers to market the unit. Once you get a Cash buyer, you explain to them that the contract price will be much higher but they will be given a buyers concession that would bring the purchase price at closing to the agreed upon price. The sale is registered at the price the Board is happy with, the transfer taxes and if applicable, the flip tax would be representative of the "registered" sale price.
Some may think this is unethical, but as long as it is done due to a traumatic event like a death in the family or extreme financial hardship, then. by all means necessary! Anyway, I don't know anyone letting $50k or $100k on the table when everything indicates an easy and quick sale. The most important factor is to make sure you and your attorney network with the management and their attorney. It is better to let the most influential people advocate for you and your cause. Once a Board says NO, it is difficult to have them change their mind.