What should I do to return the money for shares that I bought but did not pay for, and then disposed of by selling, knowing that the company owner has passed away and his children know me well, and I cannot explain the situation to them?

The price of the shares must be returned to the man's heirs along with repentance to Allah, even if indirectly, such as by sending a money order with the amount and stating that it is a debt owed to the deceased without mentioning the name.