As a general matter, a parent company will not be liable on a contract signed by its subsidiary simply because it is a wholly-owned subsidiary.  Sometimes, however, it is possible to establish some other basis for binding a parent to its subsidiary's agreement.  Such was the case in Cohen v. TNP 2008 Participating Notes Program, 2019 Cal. App. LEXIS 76.

The parent in this case had created a limited liability company to raise funds from accredited investors for various real estate investments.  The subscription agreement included an arbitration provision and the LLC agreed to arbitration with an investor.  When the nonsignatory parent did not agree, the court granted the investor's petition to compel arbitration based on the principal/agent relationship of the two companies.  In reviewing this order, the Court of Appeal adopted the standard enunciated by the Third Circuit Court of Appeals in E.I. DuPont de Nemours v. Rhone Poulenc Fiber, 269 F.3d 187 (3rd Cir. 2001):

"Not only must an arrangement exist between the two corporations so that one acts on behalf of the other and within usual agency principles, but the arrangement must be relevant to the plaintiff's claim of wrongdoing."

The Court of Appeal that the parent acted as the LLC's agent by signing the subscription agreement as "managing member".  That fact, however, was not sufficient to bind the parent to the arbitration agreement.   Based on the record, the Court found that the claims alleged against the parent arose directly from its agency relationship with the LLC and were will within the scope of the arbitration agreement. 

The foregoing is a very bare-bones description of the Cohen opinion as it relates to the question of whether a non-signatory parent may be bound by an arbitration agreement signed only by a subsidiary.  The factual circumstances and issues addressed by the Court are considerably more complicated.