Nope, they are covered most of the time by what is known as the "corporate veil".
Better explained than I can do here: https://federal-lawyer.com/when-can-a-ceo-be-held-personally-liable/
Essentially, unless they are personally doing it, they are protected. Embezzle millions and you go to jail, poison a water supply, kill thousands, give birth defects, cancer, and a myriad of other health issues to a community at large and only the corporation is liable/culpable.
Except that most firms that charge $2000/hour take the fee from the settlement, not up front, when doing civil litigation. Really only criminal law is paid directly by the client, at least in the US.