"When a California plaintiff brings an action against a foreign defendant in California court, the trial court does not possess the authority to dismiss the action on the basis of forum non conveniens. Instead, if the court determines California to be an inconvenient forum, the California court must stay the California action, in order to retain the ability to protect the California resident pending the resolution of the action in the foreign court."  (Van Keulen v. Cathay Pacific Airways, Ltd. (April 22, 2008) ___ Cal.Rptr.3d ___, 2008 WL 1799754.)  It appears settled, then, that  a case is stayed, rather than dismissed, after a foreign defendant prevails on a forum non conveniens motion.

But what happens if you don't bother to file suit in a foreign court?  The California court has discretion to dismiss the stayed action for failure to prosecute:

In this case, however, after the California court stayed the action on the basis of forum non conveniens, the California plaintiffs failed to file suit in the proper forum for over four years. The California court then granted the defendants’ motion to dismiss the California action for failure to diligently prosecute. The California plaintiffs appeal. We hold that a trial court does have the discretionary authority to dismiss for failure to diligently prosecute an action stayed on forum non conveniens grounds. We also conclude that, in this case, the trial court did not abuse its discretion by so doing.

(Slip. op., at p. 2.)  If you don't want your stayed action dismissed, be sure you file suit somewhere else, at least within 4 years of the California filing.