A "consumer," that is the party whose personal infomation is sought in the subpoea, may object. If the consumer is a party in the lawsuit, he or she may bring a motion to quash the subpoena. (See Code of Civil Procedure ("CCP") section 1985.3(g).) The motion must be served on the records custodian (the witness) and the deposition officer before the records are produced.
Consumers who are not parties may simply serve written objections to the requesting party and the proposed deponent. The objections should state the specific grounds on which the production of records should be prohibited. Such objections must be served on the party requesting the records, the records custodian and the deposition officer. See CCP sections 1985.3 (g), 1985.6(f).
"No witness or deposition officer shall be required to produce personal records after receipt of notice that the motion has been brought by a consumer, or after receipt of a written objection from a nonparty consumer, except upon order of the court...." CCP 1985.3(g).
"The party requesting a consumer's personal records may bring a motion under Section 1987.1 to enforce the subpoena within 20 days after service of the written objection." CCP 1985.3(g).
Disclamer: This response is for information purpose only and does not constitute a legal advice. This response does not create an attorney-client relationship.
See my colleague's advice, including the CCP code section governing production of personal records, which sets out the procedure and information involved in seeking personal records.
Some witnesses who receive subpoenas are more than happy to not produce anything once they receive a copy of the objection from their consumer, but your cousin needs to get a lawyer to act fast to assert objections (based on privacy rights, defects in the subpoena or its service, etc., etc.). But some witnesses are neutral or hyper-efficient and will produce records even before they need to just to get it done, so your cousin needs to act fast.
This isn't a DIY job, so your cousin should hire a lawyer ASAP.
I'm only licensed in CA. Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
Attorney Lee is correct on the law regarding this topic. It is important to note that the assertion of objections is only a "temporary" obstacle in the production of documents because the court could still overrule the objections and force the production of the documents. Therefore, as Attorney Kosly recommends, your cousin should hire an attorney right away.