Praise be to Allah.
The basic principle with regard to zakaah on shares is that if the company did not pay zakaah on its wealth for any reason, then the shareholders are obliged to pay zakaah on their wealth. If the shareholder can find out from the company's accounts about his shares and whether the company paid zakaah on its shares in the manner referred to, he should pay zakaah on his shares on that basis, because it is the basic principle with regard to the way in which zakaah on shares is to be paid.
If the shareholder cannot find that out:
If he bought shares in the company with the aim of benefitting from the annual dividend on the shares and not with the aim of trading in them, then the owner of these shares does not have to pay zakaah on the share itself; rather he has to pay zakaah on the dividend, at a rate of one quarter of one tenth after one year has passed from the day on which he took possession of the dividend.
If the shareholder bought the shares with the aim of trading in them, then he must pay the zakaah of trade goods on them. When one year has passed since they came into his possession, he must pay zakaah on their market value; if there is no market for them, he must pay zakaah on their value as estimated by experts, paying 2.5% of this value and of any profit, if the shares made any profit. End quote from Majallat Majma’ al-Fiqh al-Islami, 1/879
If there is a problem with these shares and their owner cannot dispose of them, then he should pay zakaah once, at the time of selling them or recouping their value.
Dr. Muhammad al-‘Usaymi (may Allah preserve him) was asked: O Shaykh, may Allah bless you and reward you with good, you know that there was a problem between the al-Duraybi real estate company and the government, and the shares were frozen for five years, to the point that we almost despaired, but now Allah has made things easy, and the money of the shareholders has been paid back. Does zakaah have to be paid on it? For how many years should zakaah be paid on it?
He replied: Yes, you have to pay zakaah for one year. And Allah knows best. End quote from the Shaykh’s website.
And Allah knows best.