If all elements of the group where in seperate companies, and only one of them was loss making, then you close that subsidary only. (As IO540 says, you usually pay off all the debts to save your name). The group would still be profitable and there would be no need to suspend the shares of the holding company.
This ignores the fact that in many groups there will be inter-company guarantees and composit guarantees and debentures in favour of banks and other lenders, so if there is external borrowing every company in a group will be a guarantor of the borrowing of every other company. This will result in a holding company being hit by, say, an insolvency of one of the subsidiaries and triggering the Holding Company's need to appoint an Administrator.