It’s a nightmare scenario for any business: A star employee suddenly decides to jump ship for the competition. Out the door goes years of experience, in-depth knowledge of sales and marketing plans, and a good number of hard-won customer connections.

It’s that last part, with its costly ramifications, that can cause the most immediate damage. “Customers will often follow a departing employee out the door to his or her new employer,” says Richard Avdoian, an employee-development consultant in St. Louis. “People like to stay with employees they trust.”

Longer range, the ghosting of a top-performing employee obviates any plans for ...