The company that lost the employee could go after the employee who left. You may not know whether the employee acted by themselves or if they worked in concert with their new employer.
The way I handle these kinds of cases, I know what the employee has done, so I go after them and take discovery and find out what the scope is. You usually find that the new employer has played a role. Then both parties can be sued for the claims I mentioned earlier. You will almost certainly have a claim for breach of some kind of contract with the former employee. In cases like this, the plaintiff has to move quickly to protect its IP. One of the strongest weapons you have is equitable relief, which is typically an injunction that prevents the new employer and departed employee from misusing your trade secret information.
How can an employee protect himself or herself from such lawsuits?
A number of ways. There are steps they can take before they leave a job. That is, when they're ready to leave, to announce their resignation and make a full disclosure of what they're taking and not taking. I advise people to make a list of everything they're taking from their office, such as family pictures and diplomas, and make it clear that you're not taking any [company] information with you. Employers will typically ask this of you.
I would also offer to show bags and boxes and anything you take out of the building. Give your employer an inventory and make sure your employer signs off on it. Make sure your employer has taken all necessary steps to shut off your access to all company information and systems. Access to passwords, if you have a with customer information on it, all of that should be rendered inoperable.