You ask an interesting question. I am not familiar with HFDC co-ops so I did a bit of Google research. I found that HFDC co-ops issue shares, have a proprietary lease, and generally act as a market-rate co-op except for very stringent financial requirements.

That being said, HFDC ownership is transferred by the sale and issuance of stock. When you purchased 20 years ago, you should have received a stock certificate at your closing. If you have a mortgage, the stock certificate would have been given directly to the bank holding your mortgage as collateral. Otherwise you would have received it directly.

Some buildings were rentals that converted to HFDC ownership. I don't know how the stock was issued or in what form for those.

I suggest you check all the documents you received at closing, if you can find them. You may uncover what you are looking for there. If not, contact the building's managing agent or a board member and ask them how many shares you own. You can also contact the bank that holds your mortgage (if you have one) to find out share information, but the bank may be very difficult to work with.

The only other possibility I can think of is that you are, in reality, a sub-tenant of your apartment's actual shareholder-owner. When you pay your monthly maintenance, who do you pay it to? Is it to the co-op corporation, or a private individual or different corporation? If you do not pay it directly to the co-op corporation you may be a sub-tenant and have been actually renting and not owning for all these years.

You may have to contact an attorney to help you get this straightened out. If you can't afford a private attorney, contact the Legal Aid Society. They might be able to help you for a reduced fee or no fee at all. http://www.legal-aid.org/en/civil/civilpractice/cdp/housingdevelopmentandpreservation.aspx

Good luck with your investigations.