A firm will shut down in the long run if its earning is

In the long run, a firm must cover all its costs, including both explicit costs (wages, rent, raw materials) and the implicit opportunity cost of the entrepreneur's time and capital. The return that just covers all these costs is called normal profit. Normal profit is the minimum earnings necessary to keep a firm in an industry.

If a firm's earnings fall below normal profit, the entrepreneur is earning less than what could be obtained by deploying resources in the next-best alternative use. There is no economic incentive to remain in the industry. In the long run, the firm will therefore shut down and the entrepreneur will redirect resources to more rewarding opportunities.

A firm earning supernormal (abnormal) profit is making more than the minimum required and has every reason to continue operating. A firm earning exactly normal profit is covering all costs, including opportunity costs, and will stay in the industry. A firm earning less than supernormal profit but still at or above normal profit is still viable.

The shutdown condition in the long run is therefore that earnings are less than normal profit.