Hi Kiran,
Find below the relevant extract of section-4 which governs holding and subsidiary relationship:
4. Meaning of "holding company" and "subsidiary"
(1) For the purposes of this Act, a company shall, subject to the provisions of sub-section (3), be deemed to be a subsidiary of another if, but only if –
a) that other controls the composition of its Board of directors; or
2[(b) that other –
(i) where the first-mentioned company is an existing company in respect of which the holders of preference shares issued before the commencement of this Act have the same voting rights in all respects as the holders of equity shares, exercises or controls more than half of the total voting power of such company;
(ii) where the first-mentioned company is any other company, holds more than half in nominal value of its equity share capital; or]
c) the first-mentioned company is a subsidiary of any company which is that other's subsidiary.
In your case I am presuming that public company was holding more than half in nominal value of equity share capital of private company due to which such private company becomes a public company as per section 4.
And now Holding company has sold the shares of subsidiary Company. Here I am presuming that stake is less then 50% nominal value of equity share capital of private company. In this situation we can say that public company status of such private has lost and again it becomes a purely private company.
Best Regards