I've scanned procedures for handling unclaimed safe deposit boxes and stocks from a number of states(though not NY)--none handle things in any way similar to the way you have described. They tend to hold the materials and assets for eventual return to the box holders or their heirs.

They are generally required to keep records of the contents of the box, as well as the costs associated with holding and managing the contents. You could start out by requesting copies of all their records, and proceed from there.

As to the stock, Apple keeps records of their shareholders stake, and details on the date acquired and sold. Call them. There are laws governing the exchange of shares of public stocks, and it is unlikely that they could have been sold for anything other than their market value on the day they were sold.

Given that Apple went public in 1980, it would have been impossible for the stocks to have been older than that--also, Apple never really made a "word processor", per se--

Given that you didn't know about the safe deposit box, I am curious to know how you came to know what was in it--