Usually you just hear about people suing the company, they are easier to collect from. Often they have insurance that will pay out a claim that is faster to pursue than a lawsuit. And if the damages are really large a single employee could go bankrupt. Also because the company is vicariously liable for the actions of their employees in the scope of their duties.
But anyone that personally causes damage through negligence or intentional acts can be sued personally as well. If the employer is bankrupt the employees involved would be the only ones pursued. And these damages are relatively small individually, bankruptcy is not an issue.
Also there are some exceptions to the limited liability for company owners or directors like for illegal activity and fraud.