A fight over whether IBM employees can sue over the falling value of company shares in their 401(k) plan could lead to a wild west of litigation against employers if the Supreme Court affirms a regional appeals court ruling or decides not to take the case.

Attorneys say companies would risk getting sued every time their stocks drop if a ruling in the employee’s favor from the New York-based U.S. Court of Appeals for the Second Circuit is left standing. Lawsuits over employer stock brought under the Employee Retirement Income Security Act—the federal law that protects retirement funds—can cost companies...