Probably not. Even if we assume that the case had something to do with the member’s role within the organization and was not a totally personal and unrelated matter, the whole idea of D & O insurance is to protect those who have been brought into a legal proceeding because of their role with the organization and have to defend against allegations of misconduct.  Such insurance does not normally pay the costs of bringing an action.  It is more likely that the member defendant would be protected by the D & O insurance than that the director could collect costs of prosecution.

Quite apart from your insurance, state nonprofit corporation laws contain rules for indemnification (i.e. paying the defense and legal costs) of people brought into litigation involving their conduct with the organization.  Most of the statute is usually permissive, although organizations often, by language in their bylaws, commit themselves to indemnification beyond what they are legally required to do.  (See Ready Reference Page:  “Bylaws Function as ‘Constitution of Nonprofit Corporation”)  Your member ought to check your bylaws to see if he or she is personally protected. 

In some states, such as Pennsylvania, a nonprofit corporation is obligated to pay the defense costs of “a representative” of the corporation who actually wins a suit for which indemnification would be permitted.  Since most suits are settled without a final ruling, this provision is not often invoked, but, without knowing all of the facts of this situation, it sounds as though it might be applicable here.