The Attorney-client privilege is a rather significant aspect of the American legal system. It is what allows a client to speak candidly with a lawyer so that a solid defense can be built - without it, a client would be less likely to be candid with his representative.
The privilege is held by the client, not the lawyer. Privilege can only be waived by the client, generally. There are, of course, exceptions and limits, but the general rule is an important one. This rule transends death of the client. Simply dying does not remove the privilege, indeed it would appear to lock it in place, as a client can't consent to revealing privileged information if the client isn't living. Why would this matter? Because otherwise a client who knows that what he says might be available in the event of his death could decide not to be completely candid. The interest here is to defend the client and the client's interests. Privilege = good.