There is usually no advantage to shutting down a business immediately after the owner dies, unless it's a single-person business. The survivors should be afforded some flexibility to continue its operation until it can be liquidated or sold by them on the most favorable terms. Having a succession plan in place will help to deal with the problems that arise when there are several owners and they can't agree on whether to keep, sell or liquidate the business after one owner leaves or dies. Someone who inherits a business interest often doesn't have any input in the management of the business, which is usually left to the surviving original owners. This means the beneficiaries must rely on the controlling owners for a return on their investment.
Owners often fail to develop a management succession plan.
It's essential to the survival of the business that successor management, whether from the family or otherwise, be available to take over. Your business may not be one that can be split equally among children. Those who are active in the business may see inheriting it as critical to their future motivation. Those not involved in the business may not be as interested. Perhaps the entire family feels entitled to equal shares of the business.